--- a/semantics/prov-sem-review-20130226.html Fri Mar 01 17:58:46 2013 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,3084 +0,0 @@
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- <body><div class="head">
- <p>
-
- <a href="http://www.w3.org/"><img src="https://www.w3.org/Icons/w3c_home" alt="W3C" height="48" width="72"></a>
-
- </p>
- <h1 class="title" id="title">Semantics of the PROV Data Model</h1>
-
- <h2 id="w3c-editor-s-draft-25-february-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Editor's Draft 25 February 2013</h2>
- <dl>
-
- <dt>This version:</dt>
- <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
- <dt>Latest published version:</dt>
- <dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd>
-
-
- <dt>Latest editor's draft:</dt>
- <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
-
-
-
-
-
-
-
-
- <dt>Editor:</dt>
- <dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
-
-
- </dl>
-
-
-
-
-
- <p class="copyright">
- <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> ©
- 2012-2013
-
- <a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
- (<a href="http://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
- <a href="http://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
- <a href="http://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>), All Rights Reserved.
- <abbr title="World Wide Web Consortium">W3C</abbr> <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
- <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and
- <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.
- </p>
-
-
- <hr>
-</div><div style="visibility: hidden; overflow: hidden; position: absolute; top: 0px; height: 1px; width: auto; padding: 0px; border: 0px none; margin: 0px; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal;"><div id="MathJax_Hidden"></div></div><div style="display: none;" id="MathJax_Message"></div>
-
- <section class="introductory" id="abstract"><h2>Abstract</h2>
-<p>
-Provenance is information about entities, activities, and people
-involved in producing a piece of data or thing, which can be used to
-form assessments about its quality, reliability or
-trustworthiness. PROV-DM is the conceptual data model that forms a
-basis for the <abbr title="World Wide Web Consortium">W3C</abbr> provenance (PROV) family of specifications.
-</p>
-
-
-<p> This document presents a model-theoretic semantics for the PROV
-data model (called the <dfn id="dfn-reference-semantics">reference semantics</dfn>), viewing
-PROV-DM statements as atomic formulas in the sense of first-order
-logic, and viewing the constraints and inferences specified in
-PROV-CONSTRAINTS as a first-order theory. It is shown that the
-first-order theory is sound with respect to the reference semantics.
-This information may be useful to researchers or users of PROV to
-understand the intended meaning and use of PROV for modeling
-information about the actual history, derivation or evolution of Web
-resources. It may also be useful for development of additional
-constraints or inferences for reasoning about PROV or integration of
-PROV with other Semantic Web vocabularies. It is <b>not</b> proposed
-as a canonical or required semantics of PROV and does not place any
-constraints on use of PROV.</p>
-
-<p>The PROV Document Overview describes the overall state of PROV, and should be read before other PROV documents.</p>
-</section><section id="sotd" class="introductory"><h2>Status of This Document</h2>
-
-
-
- <p>
- <em>This section describes the status of this document at the time of its publication. Other
- documents may supersede this document. A list of current <abbr title="World Wide Web Consortium">W3C</abbr> publications and the latest revision
- of this technical report can be found in the <a href="http://www.w3.org/TR/"><abbr title="World Wide Web Consortium">W3C</abbr> technical reports
- index</a> at http://www.w3.org/TR/.</em>
- </p>
-
-<h4 id="prov-family-of-documents">PROV Family of Documents</h4>
-This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
-interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below. Please consult the [<cite><a href="#bib-PROV-OVERVIEW" class="bibref">PROV-OVERVIEW</a></cite>] for a guide to reading these documents.
-<ul>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">PROV-OVERVIEW</a> (To be published as Note), an overview of the PROV family of documents [<cite><a href="#bib-PROV-OVERVIEW" class="bibref">PROV-OVERVIEW</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> (To be published as Note), a primer for the PROV data model [<cite><a href="#bib-PROV-PRIMER" class="bibref">PROV-PRIMER</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [<cite><a href="#bib-PROV-O" class="bibref">PROV-O</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [<cite><a href="#bib-PROV-N" class="bibref">PROV-N</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model (this document);</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note), an XML schema for the PROV data model [<cite><a href="#bib-PROV-XML" class="bibref">PROV-XML</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [<cite><a href="#bib-PROV-AQ" class="bibref">PROV-AQ</a></cite>]; </li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a href="#bib-PROV-DICTIONARY" class="bibref">PROV-DICTIONARY</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [<cite><a href="#bib-PROV-DC" class="bibref">PROV-DC</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a href="#bib-PROV-SEM" class="bibref">PROV-SEM</a></cite>];</li>
-<li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles [<cite><a href="#bib-PROV-LINKS" class="bibref">PROV-LINKS</a></cite>].</li>
-</ul>
-
-
- <p>
- This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as an Editor's Draft.
-
-
- If you wish to make comments regarding this document, please send them to
- <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a>
- (<a href="mailto:public-prov-comments-request@w3.org?subject=subscribe">subscribe</a>,
- <a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archives</a>).
-
-
-
-
- All comments are welcome.
-
-
- </p><p>
- Publication as an Editor's Draft does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
- This is a draft document and may be updated, replaced or obsoleted by other documents at
- any time. It is inappropriate to cite this document as other than work in progress.
- </p>
-
-
- <p>
-
- This document was produced by a group operating under the
- <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
-
-
-
-
- <abbr title="World Wide Web Consortium">W3C</abbr> maintains a <a href="http://www.w3.org/2004/01/pp-impl/46974/status" rel="disclosure">public list of any patent disclosures</a>
-
- made in connection with the deliverables of the group; that page also includes instructions for
- disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains
- <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a> must disclose the
- information in accordance with <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section
- 6 of the <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
-
-
- </p>
-
-
-
-
-</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a class="tocxref" href="#introduction"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#purpose"><span class="secno">1.1 </span>Purpose of this document</a></li><li class="tocline"><a class="tocxref" href="#structure-of-this-document"><span class="secno">1.2 </span>Structure of this document</a></li><li class="tocline"><a class="tocxref" href="#audience"><span class="secno">1.3 </span> Audience </a></li></ul></li><li class="tocline"><a class="tocxref" href="#basics"><span class="secno">2. </span> Basics </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#identifiers"><span class="secno">2.1 </span> Identifiers </a></li><li class="tocline"><a class="tocxref" href="#times-and-intervals"><span class="secno">2.2 </span> Times and Intervals </a></li><li class="tocline"><a class="tocxref" href="#attributes-and-values"><span class="secno">2.3 </span> Attributes and Values </a></li><li class="tocline"><a class="tocxref" href="#formulas"><span class="secno">2.4 </span>Atomic Formulas</a></li><li class="tocline"><a class="tocxref" href="#first-order-formulas"><span class="secno">2.5 </span>First-Order Formulas</a></li></ul></li><li class="tocline"><a class="tocxref" href="#structures"><span class="secno">3. </span> Structures and Interpretations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#things-1"><span class="secno">3.1 </span> Things </a></li><li class="tocline"><a class="tocxref" href="#objects-1"><span class="secno">3.2 </span> Objects </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#entities-1"><span class="secno">3.2.1 </span> Entities </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#plans-1"><span class="secno">3.2.1.1 </span> Plans </a></li></ul></li><li class="tocline"><a class="tocxref" href="#actvities"><span class="secno">3.2.2 </span> Actvities </a></li><li class="tocline"><a class="tocxref" href="#agents-1"><span class="secno">3.2.3 </span> Agents </a></li><li class="tocline"><a class="tocxref" href="#interactions-1"><span class="secno">3.2.4 </span> Interactions </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#events-1"><span class="secno">3.2.4.1 </span> Events </a></li><li class="tocline"><a class="tocxref" href="#associations-1"><span class="secno">3.2.4.2 </span> Associations </a></li><li class="tocline"><a class="tocxref" href="#communications"><span class="secno">3.2.4.3 </span>Communications</a></li><li class="tocline"><a class="tocxref" href="#delegations"><span class="secno">3.2.4.4 </span>Delegations</a></li><li class="tocline"><a class="tocxref" href="#derivations-1"><span class="secno">3.2.4.5 </span> Derivations </a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#relations"><span class="secno">3.3 </span> Relations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#derivation-paths-and-derivedfrom"><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </a></li></ul></li><li class="tocline"><a class="tocxref" href="#putting-it-all-together"><span class="secno">3.4 </span> Putting it all together </a></li><li class="tocline"><a class="tocxref" href="#interpretations"><span class="secno">3.5 </span> Interpretations </a></li></ul></li><li class="tocline"><a class="tocxref" href="#semantics"><span class="secno">4. </span> Semantics </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#satisfaction"><span class="secno">4.1 </span> Satisfaction </a></li><li class="tocline"><a class="tocxref" href="#attribute-matching"><span class="secno">4.2 </span> Attribute matching </a></li><li class="tocline"><a class="tocxref" href="#semantics-of-element-formulas"><span class="secno">4.3 </span> Semantics of Element Formulas </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#entity"><span class="secno">4.3.1 </span> Entity </a></li><li class="tocline"><a class="tocxref" href="#activity"><span class="secno">4.3.2 </span> Activity </a></li><li class="tocline"><a class="tocxref" href="#agent"><span class="secno">4.3.3 </span> Agent </a></li></ul></li><li class="tocline"><a class="tocxref" href="#semantics-of-relations"><span class="secno">4.4 </span> Semantics of Relations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#generation"><span class="secno">4.4.1 </span> Generation </a></li><li class="tocline"><a class="tocxref" href="#use"><span class="secno">4.4.2 </span> Use </a></li><li class="tocline"><a class="tocxref" href="#invalidation"><span class="secno">4.4.3 </span> Invalidation </a></li><li class="tocline"><a class="tocxref" href="#association"><span class="secno">4.4.4 </span> Association </a></li><li class="tocline"><a class="tocxref" href="#start-formulas"><span class="secno">4.4.5 </span> Start Formulas </a></li><li class="tocline"><a class="tocxref" href="#end"><span class="secno">4.4.6 </span> End </a></li><li class="tocline"><a class="tocxref" href="#attribution"><span class="secno">4.4.7 </span> Attribution </a></li><li class="tocline"><a class="tocxref" href="#communication"><span class="secno">4.4.8 </span>Communication</a></li><li class="tocline"><a class="tocxref" href="#responsibility"><span class="secno">4.4.9 </span> Responsibility </a></li><li class="tocline"><a class="tocxref" href="#derivation"><span class="secno">4.4.10 </span> Derivation </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#precise"><span class="secno">4.4.10.1 </span> Precise </a></li><li class="tocline"><a class="tocxref" href="#imprecise"><span class="secno">4.4.10.2 </span> Imprecise </a></li></ul></li><li class="tocline"><a class="tocxref" href="#influence"><span class="secno">4.4.11 </span>Influence</a></li><li class="tocline"><a class="tocxref" href="#specialization"><span class="secno">4.4.12 </span> Specialization </a></li><li class="tocline"><a class="tocxref" href="#alternate"><span class="secno">4.4.13 </span> Alternate </a></li><li class="tocline"><a class="tocxref" href="#membership"><span class="secno">4.4.14 </span> Membership </a></li></ul></li><li class="tocline"><a class="tocxref" href="#auxiliary-formulas"><span class="secno">4.5 </span>Auxiliary formulas</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#equals"><span class="secno">4.5.1 </span>Equals</a></li><li class="tocline"><a class="tocxref" href="#precedes-and-strictly-precedes"><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</a></li><li class="tocline"><a class="tocxref" href="#notnull"><span class="secno">4.5.3 </span>notNull</a></li><li class="tocline"><a class="tocxref" href="#typeof"><span class="secno">4.5.4 </span>typeOf</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#theory"><span class="secno">5. </span> Inferences and Constraints </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#inferences"><span class="secno">5.1 </span>Inferences</a></li><li class="tocline"><a class="tocxref" href="#constraints"><span class="secno">5.2 </span>Constraints</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#uniqueness-constraints"><span class="secno">5.2.1 </span>Uniqueness constraints</a></li><li class="tocline"><a class="tocxref" href="#ordering-constraints"><span class="secno">5.2.2 </span>Ordering constraints</a></li><li class="tocline"><a class="tocxref" href="#typing-constraints"><span class="secno">5.2.3 </span>Typing constraints</a></li><li class="tocline"><a class="tocxref" href="#impossibility-constraints"><span class="secno">5.2.4 </span>Impossibility constraints</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#soundness"><span class="secno">6. </span>Soundness</a></li><li class="tocline"><a class="tocxref" href="#acknowledgements"><span class="secno">A. </span>Acknowledgements</a></li><li class="tocline"><a class="tocxref" href="#references"><span class="secno">B. </span>References</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#informative-references"><span class="secno">B.1 </span>Informative references</a></li></ul></li></ul></section>
-
-
-
-
-
-
- <section id="introduction">
- <!--OddPage--><h2><span class="secno">1. </span>Introduction</h2>
-
-<p>
-Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing.
-This document complements
- the PROV-DM specification [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>] that defines a data model for
- provenance on the Web, and the PROV-CONSTRAINTS specification
-[<cite><a href="#bib-PROV-CONSTRAINTS" class="bibref">PROV-CONSTRAINTS</a></cite>] that
-specifies definitions, inferences, and constraints that can be used to
-reason about PROV documents, or determine their validity. This document
-provides a reference formal semantics of PROV, providing a formal
-counterpart to the informal descriptions and motivations given
-elsewhere in PROV specifications.</p>
-
-
-
-<!--
-<section id="conventions">
-<h3>Conventions</h3>
-
-
-<p>In this document, logical formulas contain variables written as
- lower-case identifiers. Some of these variables are written
- beginning with the underscore character <span
- class="name">_</span>, by convention, to indicate that they
- appear only once in the formula. Such variables are
- provided merely as an aid to the reader. </p>
-
-</section>
--->
-
-<section id="purpose">
-
-<h3><span class="secno">1.1 </span>Purpose of this document</h3>
-
-</section>
-<p>The PROV-DM and PROV-CONSTRAINTS give motivating examples that
-provide an intuition about the meaning of the constructs. For some
-concepts, such as use, start, end, generation/invalidation, and
-derivation, the meaning is either obvious or situation-dependent.
-However, during the development of PROV, the importance of additional
-concepts became evident, but the intuitive meaning or correct use of
-these concepts were not clear. For example, the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-1-Frame" class="MathJax"><nobr><span id="MathJax-Span-1" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-1" type="math/tex">alternateOf</script> and
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-2-Frame" class="MathJax"><nobr><span id="MathJax-Span-14" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-22" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-23" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-24" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-25" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-26" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-27" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-28" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-29" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-30" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-31" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-2" type="math/tex">specializationOf</script> relations are used in PROV to relate different
-entities that present aspects of "the same thing".
-Over time the working group came to a
-consensus about these concepts and how they are to be used, but this
-understanding is based on abstract notions that are not explicit in
-PROV documents; instead, some of their properties are captured
-formally through certain constraints and inferences, while others are
-not captured in PROV specifications at all.
-</p>
-
-<p>The purpose of this document is to present the working group's
-consensus view of the semantics of PROV, using tools from mathematical
-logic, principally model theory (though our use of these tools is lightweight). This information may be useful to users for understanding the
-intent behind certain features of PROV, to researchers investigating
-richer forms of reasoning over provenance, or to future efforts
-building upon PROV. It is intended as an exploration of a <b>reference</b>
-semantics for PROV, not a definitive specification of the <b>only</b>
-semantics of PROV. </p>
-
-<p> Nevertheless, the reference semantics does have appealing
-properties. Specifically, it provides a declarative counterpart to
-the operational definition of validity taken in PROV-CONSTRAINTS. In
-the specification, validity is defined via a normalization process
-followed by constraint checking on the normal form. This approach was adopted
-to keep the specification closer to implementations, although other
-implementations are possible and allowed. In addition to providing a
-reference semantics, this document shows that the operational
-presentation of PROV validity checking is sound with respect to
-declarative presentation adopted here. This could help justify
-alternative approaches to validity checking.</p>
-
-<section id="structure-of-this-document"> <h3><span class="secno">1.2 </span>Structure of this document</h3> <p>
-
-</p>
-
-<ul>
- <li><a href="#basics">Section 2</a> summarizes the basic concepts
- from mathematical logic used in the semantics, recapitulates how
- PROV statements can be viewed as atomic formulas, and introduces
- some auxiliary formulas.</li>
- <li><a href="#structures">Section 3</a> presents the mathematical
- structures used for situations that PROV statements can
- describe.</li>
- <li><a href="#semantics">Section 4</a> defines the semantics of PROV
- statements and auxiliary formulas, indicating when a given formula
- is satisfied in a structure.</li>
- <li><a href="#theory">Section 5</a> presents the inferences and
- constraints from PROV-CONSTRAINTS as first-order formulas, and gives
- brief justifications for their soundness.</li>
- <li><a href="#soundness">Section 6</a> relates the PROV notion of
- validity to the logical notion of consistency. A PROV instance is
- valid if and only if its corresponding first-order theory is
- satisfiable.</li>
-</ul>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">
- Completeness direction above doesn't hold for current semantics,
- because attributes assumed to be single-valued; for
- example, <span class="MathJax_Preview">entity(id,[a=1,a=2])</span><script id="MathJax-Element-3" type="math/tex">entity(id,[a=1,a=2])</script> is valid but doesn't have a
- reference model.
- </div></div>
-
-</section>
-<section id="audience">
-<h3><span class="secno">1.3 </span> Audience </h3>
-
-
-<p>This document assumes familiarity with [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>] and
- [<cite><a href="#bib-PROV-CONSTRAINTS" class="bibref">PROV-CONSTRAINTS</a></cite>] and employs (a
- simplified form of)
-[<cite><a href="#bib-PROV-N" class="bibref">PROV-N</a></cite>] notation. In particular it assumes familiarity with the concepts
- from logic, and the relationship between PROV statements and
- instances and first-order formulas and theories, respectively,
- presented in <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/#overview">Section 2.5</a> of PROV-CONSTRAINTS.
-</p>
-
- <p>This document may be useful to users of PROV who have a formal
- background and are interested in the rationale for some of the
- constructs of PROV; for resaerchers investigating extensions of PROV
- or alternative approaches to reasoning about PROV; or for future
- efforts on provenance standardization. </p>
-
- </section>
-
- </section>
-
-
- <!--
-
-<section id="overview">
-<h2> Overview </h2>
-
-
-<p>The idea of this document is to sketch what aspects of the provenance model can be formalized and how they can be formalized, as a first step towards establishing a consensus on the (intended) meaning of the components of the model and the consistency constraints or inferences that can be applied to the model to distinguish valid from invalid provenance records.</p>
-
-<p>The <a href="http://www.w3.org/TR/prov-constraints/">PROV-CONSTRAINTS</a> document contains formal content specifying a notion of validity (approximately, logical consistency) for PROV documents. The formal semantics, PROV-SEM, is planned for release as a W3C Note that will complement the procedural specification in PROV-CONSTRAINTS with a declarative specification formulated in terms of first-order logic. The formal semantics is <b>work in progress</b>. The drafts below are intermediate stages and some of them are out of date.
-</p>
-
-<h3> Status </h3>
-
-<p>
-This is work in progress. The semantics is being updated to be consistent with the Candidate Recommendation of PROV. The plan is to release the semantics as a Note over the next few months. At that point, the wiki pages containing drafts of the semantics will be superseded.
-</p>
-
-
-<h3> Idea of the semantics </h3>
-
-<p>As a starting point, I will assume that we intend the statements made in a PROV-DM instance to be intended to describe one, consistent state of the world, much like a logical formula is said to be satisfied in a mathematical model. That is, I propose an approach similar to that taken in model theory, where the PROV-DM instance corresponds to a formula or theory of a logic, and the semantics corresponds to what logicians call a model.</p>
-
-<p>For example, the formula $\forall x. P(x) \Rightarrow Q(x)$ is satisfied in a mathematical model where the relation $P$ denotes a set of elements that is contained in that denoted by $Q$. Here, the goal is to come up with a plausible "intended model" for interpreting PROV-DM instances, where the formulas are statements in PROV-DM and the individuals are things and agents. This is complicated by the fact that many statements about provenance involve talking about objects that change over time.</p>
-
-<p>The word "world" is used in PROV-DM to talk about the actual state
-of affairs that the PROV-DM instance describes, which is what I would
-usually call a "model". The word "model" is used in PROV-DM mainly in
-the sense of "data model", that is, to talk about what I would
-otherwise call the syntax of PROV-DM. To avoid confusion with the
-uses of terms in PROV-DM, I will use "structure" to describe the
-mathematical structure that corresponds to actual state of affairs.
-We use the term "model" to describe a structure that satisfies a given
-theory; this sense of "model" does not mean "data model".</p>
-
-<h3> Axiomatization and relationship to PROV-CONSTRAINTS </h3>
-
-<p>One goal of the semantics is to link the procedural specification of validity and equivalence with traditional notions of logical consistency and equivalence of theories, for example in first-order logic. A first-order axiomatization that corresponds to the formal constraints and is sound for reasoning about the models described below is in progress at the end of the document.
-</p>
-</section>
--->
-
-<section id="basics">
-<!--OddPage--><h2><span class="secno">2. </span> Basics </h2>
-
-
-
-
-
-<section id="identifiers">
-<h3><span class="secno">2.1 </span> Identifiers </h3>
-
-<p>A lowercase symbol <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-4-Frame" class="MathJax"><nobr><span id="MathJax-Span-54" class="math"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-55" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-56" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-57" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-58" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-59" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-60" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-61" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-62" class="mo">.</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-4" type="math/tex">x,y,...</script> on its own denotes an identifier.
-Identifiers may or may not be URIs. Identifiers are viewed as variables in logic (or blank nodes in RDF): just because we have two different identifiers <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-5-Frame" class="MathJax"><nobr><span id="MathJax-Span-63" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-64" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-65" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-5" type="math/tex">x</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-6-Frame" class="MathJax"><nobr><span id="MathJax-Span-66" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.55em); top: -2.57em; left: 0em;"><span id="MathJax-Span-67" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-68" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-6" type="math/tex">y</script> doesn't tell us that they denote different things, since we could discover that they are actually the same later. We write <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-7-Frame" class="MathJax"><nobr><span id="MathJax-Span-69" class="math"><span style="display: inline-block; position: relative; width: 75px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-70" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-71" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-72" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-73" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-74" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-75" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-76" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-77" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-78" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-79" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-80" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-81" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-7" type="math/tex">Identifiers</script> for the set of identifiers of interest in a given situation (typically, the set of identifiers present in the PROV instance of interest).
-</p>
-</section>
-
-<section id="times-and-intervals">
-<h3><span class="secno">2.2 </span> Times and Intervals </h3>
-
-<p>We assume a linearly ordered set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-8-Frame" class="MathJax"><nobr><span id="MathJax-Span-82" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-83" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-84" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-85" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-86" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-87" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-88" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-89" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-90" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-91" class="mo">≤</span><span style="font-family: STIXGeneral;" id="MathJax-Span-92" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-8" type="math/tex">(Times,\leq)</script> of time instants. For convenience we assume the order is total or linear order, corresponding to a linear timeline; however, PROV does not assume that time is linear and events could be partially ordered and not necessarily reconciled to a single global clock.
-</p>
-<p>We also consider a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-9-Frame" class="MathJax"><nobr><span id="MathJax-Span-93" class="math"><span style="display: inline-block; position: relative; width: 62px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-94" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-95" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-96" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-97" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-98" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-99" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-100" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-101" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-102" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-103" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-9" type="math/tex">Intervals</script> of closed intervals of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-10-Frame" class="MathJax"><nobr><span id="MathJax-Span-104" class="math"><span style="display: inline-block; position: relative; width: 108px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.705em, 1000em, 2.934em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-105" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-106" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-108" class="mo">∣</span><span style="padding-left: 0.313em;" id="MathJax-Span-109" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-111" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-112" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-113" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-114" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-115" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-117" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-118" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.066em; vertical-align: -0.265em;"></span></span></nobr></span><script id="MathJax-Element-10" type="math/tex">\{t \mid t_1 \leq t \leq t_2\}</script>.
-</p>
-</section>
-
-<section id="attributes-and-values">
-<h3><span class="secno">2.3 </span> Attributes and Values </h3>
-
-<p>We assume a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-11-Frame" class="MathJax"><nobr><span id="MathJax-Span-119" class="math"><span style="display: inline-block; position: relative; width: 69px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-120" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-121" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-122" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-123" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-124" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-125" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-126" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-127" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-129" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-130" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-11" type="math/tex">Attributes</script> of attribute labels and a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-12-Frame" class="MathJax"><nobr><span id="MathJax-Span-131" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.45em); top: -2.57em; left: 0em;"><span id="MathJax-Span-132" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-133" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-134" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-135" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-136" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-137" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-138" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-12" type="math/tex">Values</script>
-of possible values of attributes. To allow for the fact that some
-attributes can have undefined or multiple values, we sometimes use the set
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-13-Frame" class="MathJax"><nobr><span id="MathJax-Span-139" class="math"><span style="display: inline-block; position: relative; width: 63px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-141" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-142" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-143" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-144" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-145" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-146" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-147" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-148" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-13" type="math/tex">P(Value)</script>, that is, the set of sets of values.
-</p> </section>
-
-<section id="formulas">
-<h3><span class="secno">2.4 </span>Atomic Formulas</h3>
-
-<p>The following atomic formulas correspond to the statements of PROV-DM. We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-14-Frame" class="MathJax"><nobr><span id="MathJax-Span-149" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-150" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-151" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-152" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-153" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-154" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-155" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-157" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-158" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-159" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-160" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-161" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-162" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-163" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-164" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-165" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-14" type="math/tex">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-15-Frame" class="MathJax"><nobr><span id="MathJax-Span-166" class="math"><span style="display: inline-block; position: relative; width: 107px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-168" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-169" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-170" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-171" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-172" class="mo">;</span><span style="padding-left: 0.188em;" id="MathJax-Span-173" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-174" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-175" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-176" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-177" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-178" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-179" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-180" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-181" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-182" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-15" type="math/tex">r(id;a_1,\ldots,a_n)</script>.
-</p>
-<p>Each parameter is either an identifier, a constant (e.g. a time or other literal value in an attribute list), or a null symbol "-". Null symbols can only appear in the specified arguments in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-16-Frame" class="MathJax"><nobr><span id="MathJax-Span-183" class="math"><span style="display: inline-block; position: relative; width: 135px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-184" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-185" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-187" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-188" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-189" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-190" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-191" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-192" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-193" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-194" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-196" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-197" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-198" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-199" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-200" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-201" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-16" type="math/tex">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-17-Frame" class="MathJax"><nobr><span id="MathJax-Span-202" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-203" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-204" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-206" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-207" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-208" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-209" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-210" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-211" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-212" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-213" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-214" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-215" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-216" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-217" class="mi">m</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-17" type="math/tex">wasDerivedFrom</script>, as shown in the grammar below.
-</p>
-<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-18-Frame" class="MathJax"><nobr><span id="MathJax-Span-218" class="math"><span style="display: inline-block; position: relative; width: 487px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(-20.206em, 1000em, 23.795em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-219" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-220" class="mtable"><span style="display: inline-block; position: relative; width: 28.126em; height: 0px;"><span style="position: absolute; clip: rect(22.201em, 1000em, 65.879em, -0.526em); top: -44.334em; left: 0em;"><span style="display: inline-block; position: relative; width: 7.477em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -23.845em; right: 0em;"><span id="MathJax-Span-221" class="mtd"><span id="MathJax-Span-222" class="mrow"><span style="font-family: STIXGeneral; 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font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1048" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1049" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.553em); top: 5.57em; left: 0em;"><span id="MathJax-Span-1074" class="mtd"><span id="MathJax-Span-1075" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1076" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1077" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1078" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.863em, 1000em, 2.951em, -0.553em); top: 6.903em; left: 0em;"><span id="MathJax-Span-1086" class="mtd"><span id="MathJax-Span-1087" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1088" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1089" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1090" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.553em); top: 8.235em; left: 0em;"><span id="MathJax-Span-1098" class="mtd"><span id="MathJax-Span-1099" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1100" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1101" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1102" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.512em); top: 9.574em; left: 0em;"><span id="MathJax-Span-1110" class="mtd"><span id="MathJax-Span-1111" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1112" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1113" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1114" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1115" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1116" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1117" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1118" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1119" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1120" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1121" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.488em); top: 10.879em; left: 0em;"><span id="MathJax-Span-1129" class="mtd"><span id="MathJax-Span-1130" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1131" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1132" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1133" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1134" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1135" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1136" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1137" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1138" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1139" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1141" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1142" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.733em, 1000em, 2.902em, -0.438em); top: 12.198em; left: 0em;"><span id="MathJax-Span-1153" class="mtd"><span id="MathJax-Span-1154" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1155" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1156" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1157" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-1159" class="msubsup"><span style="display: inline-block; position: relative; width: 0.811em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1160" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1161" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1162" class="mo">=</span><span style="padding-left: 0.313em;" id="MathJax-Span-1163" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1164" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1165" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1166" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-1167" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-1168" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1169" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-1172" class="msubsup"><span style="display: inline-block; position: relative; width: 0.811em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1173" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1174" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1175" class="mo">=</span><span style="padding-left: 0.313em;" id="MathJax-Span-1176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1177" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1178" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1179" class="mo">]</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.495em); top: 13.458em; left: 0em;"><span id="MathJax-Span-1189" class="mtd"><span id="MathJax-Span-1190" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1192" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1194" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1196" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.509em); top: 14.79em; left: 0em;"><span id="MathJax-Span-1204" class="mtd"><span id="MathJax-Span-1205" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1207" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1209" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1210" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1211" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1213" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: 16.122em; left: 0em;"><span id="MathJax-Span-1221" class="mtd"><span id="MathJax-Span-1222" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1223" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1224" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1225" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1226" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: 17.461em; left: 0em;"><span id="MathJax-Span-1235" class="mtd"><span id="MathJax-Span-1236" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1237" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1238" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1239" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1240" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1241" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1242" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1243" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1245" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1246" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1247" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1250" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1251" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.601em); top: 18.799em; left: 0em;"><span id="MathJax-Span-1259" class="mtd"><span id="MathJax-Span-1260" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1261" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1262" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1263" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1264" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1265" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1266" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1267" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1268" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1269" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1270" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1271" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1272" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1273" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1274" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1276" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1277" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1278" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1279" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1280" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 44.509em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 46.831em; vertical-align: -23.148em;"></span></span></nobr></span></div><script id="MathJax-Element-18" type="math/tex; mode=display">
-\begin{array}{rcl}
- atomic\_formula & {::=}& element\_formula\\
- & | & relation\_formula\\
- & | & auxiliary\_formula\\
- element\_formula
- &{::=} &entity(id,attrs) \\
- & |& activity(id,st,et,attrs)\\
- & |& agent(id,attrs)\\
- relation\_formula
- &{::=}& wasGeneratedBy(id,e,a,t,attrs)\\
- & |& used(id,e,a,t,attrs)\\
- & |& wasInvalidatedBy(id,e,a,t,attrs)\\
- & |& wasStartedBy(id,a_2,e,a_1,attrs)\\
- & |& wasEndedBy(id,a_2,e,a_1,attrs)\\
- & |& wasAssociatedWith(id,ag,act,pl,attrs)\\
- & |& wasAssociatedWith(id,ag,act,-,attrs)\\
- & |& wasAttributedTo(id,e,ag,attrs)\\
- & |& actedOnBehalfOf(if,ag_2,ag_1,act,attrs)\\
- & |& wasInformedBy(id,a_2,a_1,attrs)\\
- & |& wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)\\
- & |& wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)\\
-& | & wasInfluencedBy(id,x,y,attrs)\\
- & |& alternateOf(e_1,e_2)\\
- & |& specializationOf(e_1,e_2)\\
- & | & hadMember(c,e)\\
- auxiliary\_formula
- &{::=}& x = y\\
- & | & x \prec y\\
- & | & x \preceq y\\
- & | & notNull(x)\\
- & | & typeOf(x,ty)\\
-attrs &::=& [attr_1 = v_1, \ldots,attr_n = v_n]\\
- ty &{::=}& entity \\
-&|& activity\\
-&|& agent\\
-&|& prov:Collection\\
-&|& prov:EmptyCollection
-\end{array}
-</script>
-
-</section>
-
-<section id="first-order-formulas">
-<h3><span class="secno">2.5 </span>First-Order Formulas</h3>
-
-<p>We also consider the usual connectives and quantifiers of
-first-order logic [<cite><a href="#bib-Logic" class="bibref">Logic</a></cite>].
-<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-19-Frame" class="MathJax"><nobr><span id="MathJax-Span-1281" class="math"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(-4.148em, 1000em, 7.737em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-1282" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-1283" class="mtable"><span style="display: inline-block; position: relative; width: 10.778em; height: 0px;"><span style="position: absolute; clip: rect(6.133em, 1000em, 17.695em, -0.526em); top: -12.208em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.643em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -7.787em; right: 0em;"><span id="MathJax-Span-1284" class="mtd"><span id="MathJax-Span-1285" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1286" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -7.856em; right: 0em;"><span id="MathJax-Span-1308" class="mtd"><span id="MathJax-Span-1309" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -6.656em; right: 0em;"><span id="MathJax-Span-1321" class="mtd"><span id="MathJax-Span-1322" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -5.456em; right: 0em;"><span id="MathJax-Span-1335" class="mtd"><span id="MathJax-Span-1336" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -4.118em; right: 0em;"><span id="MathJax-Span-1347" class="mtd"><span id="MathJax-Span-1348" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -2.745em; right: 0em;"><span id="MathJax-Span-1363" class="mtd"><span id="MathJax-Span-1364" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -1.371em; right: 0em;"><span id="MathJax-Span-1379" class="mtd"><span id="MathJax-Span-1380" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 0.002em; right: 0em;"><span id="MathJax-Span-1395" class="mtd"><span id="MathJax-Span-1396" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 1.34em; right: 0em;"><span id="MathJax-Span-1408" class="mtd"><span id="MathJax-Span-1409" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span></span><span style="display: inline-block; width: 0px; height: 12.208em;"></span></span><span style="position: absolute; clip: rect(6.123em, 1000em, 17.476em, -0.459em); top: -11.974em; left: 1.768em;"><span style="display: inline-block; position: relative; width: 1.285em; height: 0px;"><span style="position: absolute; clip: rect(1.936em, 1000em, 2.756em, -0.445em); top: -7.787em; left: 50%; margin-left: -0.643em;"><span id="MathJax-Span-1287" class="mtd"><span id="MathJax-Span-1288" class="mrow"><span id="MathJax-Span-1289" class="texatom"><span id="MathJax-Span-1290" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1291" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">:</span><span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -6.454em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1310" class="mtd"><span id="MathJax-Span-1311" class="mrow"><span id="MathJax-Span-1312" class="texatom"><span id="MathJax-Span-1313" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1314" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -5.254em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1323" class="mtd"><span id="MathJax-Span-1324" class="mrow"><span id="MathJax-Span-1325" class="texatom"><span id="MathJax-Span-1326" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1327" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -4.054em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1337" class="mtd"><span id="MathJax-Span-1338" class="mrow"><span id="MathJax-Span-1339" class="texatom"><span id="MathJax-Span-1340" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1341" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -2.716em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1349" class="mtd"><span id="MathJax-Span-1350" class="mrow"><span id="MathJax-Span-1351" class="texatom"><span id="MathJax-Span-1352" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1353" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -1.343em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1365" class="mtd"><span id="MathJax-Span-1366" class="mrow"><span id="MathJax-Span-1367" class="texatom"><span id="MathJax-Span-1368" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1369" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 0.031em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1381" class="mtd"><span id="MathJax-Span-1382" class="mrow"><span id="MathJax-Span-1383" class="texatom"><span id="MathJax-Span-1384" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1385" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 1.404em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1397" class="mtd"><span id="MathJax-Span-1398" class="mrow"><span id="MathJax-Span-1399" class="texatom"><span id="MathJax-Span-1400" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1401" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 2.742em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1410" class="mtd"><span id="MathJax-Span-1411" class="mrow"><span id="MathJax-Span-1412" class="texatom"><span id="MathJax-Span-1413" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1414" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 11.974em;"></span></span><span style="position: absolute; clip: rect(6.366em, 1000em, 18.134em, -0.524em); top: -12.442em; left: 4.178em;"><span style="display: inline-block; position: relative; width: 6.6em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -7.787em; left: 0em;"><span id="MathJax-Span-1292" class="mtd"><span id="MathJax-Span-1293" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1296" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1297" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1298" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1299" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1300" class="mi">_</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1301" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1303" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1304" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1305" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1306" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1307" class="mi">a</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.742em, 1000em, 2.756em, -0.467em); top: -6.454em; left: 0em;"><span id="MathJax-Span-1315" class="mtd"><span id="MathJax-Span-1316" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1317" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1318" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1319" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1320" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.518em); top: -5.254em; left: 0em;"><span id="MathJax-Span-1328" class="mtd"><span id="MathJax-Span-1329" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1330" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1331" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1332" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1333" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1334" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.478em); top: -4.054em; left: 0em;"><span id="MathJax-Span-1342" class="mtd"><span id="MathJax-Span-1343" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1344" class="mi">¬</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1345" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1346" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: -2.716em; left: 0em;"><span id="MathJax-Span-1354" class="mtd"><span id="MathJax-Span-1355" class="mrow"><span id="MathJax-Span-1356" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1357" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1358" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1359" class="mo">∧</span><span style="padding-left: 0.25em;" id="MathJax-Span-1360" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1361" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1362" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: -1.343em; left: 0em;"><span id="MathJax-Span-1370" class="mtd"><span id="MathJax-Span-1371" class="mrow"><span id="MathJax-Span-1372" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1373" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1374" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1375" class="mo">∨</span><span style="padding-left: 0.25em;" id="MathJax-Span-1376" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1377" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1378" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: 0.031em; left: 0em;"><span id="MathJax-Span-1386" class="mtd"><span id="MathJax-Span-1387" class="mrow"><span id="MathJax-Span-1388" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1389" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1390" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1391" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-1392" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1393" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1394" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.524em); top: 1.404em; left: 0em;"><span id="MathJax-Span-1402" class="mtd"><span id="MathJax-Span-1403" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1404" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1405" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1406" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1407" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.453em); top: 2.742em; left: 0em;"><span id="MathJax-Span-1415" class="mtd"><span id="MathJax-Span-1416" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1417" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1418" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1419" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1420" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 12.442em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 12.466em; vertical-align: -5.966em;"></span></span></nobr></span></div><script id="MathJax-Element-19" type="math/tex; mode=display">
-\begin{array}{rcl}
- \phi &{::=}& atomic\_formula\\
-& | & True\\
-& | & False\\
-&|& \neg~\phi\\
- &|& \phi_1 \wedge \phi_2\\
- &|& \phi_1 \vee \phi_2\\
- &|& \phi_1 \Rightarrow \phi_2\\
-&|& \forall x. \phi\\
-&|& \exists x. \phi\\
-\end{array}
-</script>
-
-
-</p></section>
-<!--
-<section>
-<h3>Instances as Theories</h3>
-<p>A PROV-DM
-instance can be viewed as a set of atomic formulas
-$\phi_1$...$\phi_n$, often called a <em>theory</em>. A theory is
-viewed as a conjunction, that is, the overall instance is considered
-to hold in a given structure if each atomic formula in it holds.</p>
-</section>
--->
-
-
-</section>
-
-
-<section id="structures">
-<!--OddPage--><h2><span class="secno">3. </span> Structures and Interpretations </h2>
-
-<section id="things-1">
-
-<h3><span class="secno">3.1 </span> Things </h3>
-
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Containment of things / collections? (for hadMember).</div></div>
-<p><em>Things</em> are things in the world. Each thing has a lifetime during which it exists and attributes whose values can change over time.
-</p>
-<p>To model this, a structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-20-Frame" class="MathJax"><nobr><span id="MathJax-Span-1421" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1422" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1423" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-20" type="math/tex">W</script> includes:
-</p>
-<div data-title="Component 1 (things)" data-count="1" class="component" id="things"><div class="ruleTitle"><a href="#things" class="internalDFN">Component 1 (things)</a></div><ol>
- <li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-21-Frame" class="MathJax"><nobr><span id="MathJax-Span-1424" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1425" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1426" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1427" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1428" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1429" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1430" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1431" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-21" type="math/tex">Things</script> of things</li>
- <li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-22-Frame" class="MathJax"><nobr><span id="MathJax-Span-1432" class="math"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1433" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1434" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1435" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1436" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1437" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1438" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1439" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1440" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1441" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1442" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1443" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1444" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1445" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1446" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1447" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1448" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1449" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1450" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1451" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1452" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1453" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1454" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1455" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1456" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1457" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1458" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-22" type="math/tex">lifetime : Things \to Intervals</script> from objects to time intervals</li>
- <li>a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-23-Frame" class="MathJax"><nobr><span id="MathJax-Span-1459" class="math"><span style="display: inline-block; position: relative; width: 349px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1460" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1461" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1462" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1463" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1464" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1465" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1466" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1467" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1468" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1469" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1470" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1471" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1472" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1473" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1474" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1476" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1477" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1478" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1479" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1480" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1481" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1483" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1484" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1485" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1486" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1487" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1488" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1489" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1490" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1491" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1492" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1493" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1494" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1495" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1496" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1497" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1498" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1499" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-23" type="math/tex">value : Things \times Attributes \times Times \to P(Values)</script>
-</li>
-</ol>
-</div>
-<p>
-The range of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-24-Frame" class="MathJax"><nobr><span id="MathJax-Span-1500" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1501" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1502" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1504" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1505" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1506" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-24" type="math/tex">value</script> is the set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-25-Frame" class="MathJax"><nobr><span id="MathJax-Span-1507" class="math"><span style="display: inline-block; position: relative; width: 70px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1508" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1509" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1510" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1511" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1512" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1513" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1514" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1515" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1516" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1517" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-25" type="math/tex">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-26-Frame" class="MathJax"><nobr><span id="MathJax-Span-1518" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1519" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1520" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1521" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1522" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1523" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1524" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-26" type="math/tex">value</script>
-is essentially a multi-valued that returns a set of values (possibly empty). When <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-27-Frame" class="MathJax"><nobr><span id="MathJax-Span-1525" class="math"><span style="display: inline-block; position: relative; width: 116px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1526" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1527" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1528" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1529" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1530" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1531" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1532" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1533" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1534" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1535" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1538" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1539" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1540" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-27" type="math/tex">value(x,a,t) =
-\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-28-Frame" class="MathJax"><nobr><span id="MathJax-Span-1541" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1542" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1543" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-28" type="math/tex">a</script> is undefined for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-29-Frame" class="MathJax"><nobr><span id="MathJax-Span-1544" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1545" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1546" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-29" type="math/tex">x</script> at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-30-Frame" class="MathJax"><nobr><span id="MathJax-Span-1547" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1548" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-30" type="math/tex">t</script>.</p>
-
-<p>Note that this description does not say what the structure of a
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-31-Frame" class="MathJax"><nobr><span id="MathJax-Span-1550" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1551" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1552" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1553" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1554" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1555" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1556" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-31" type="math/tex">Thing</script> is, only how it may be described in terms of its time interval
-and attribute values. An object could just be a record of fixed
-attribute values; it could be a bear; it could be the Royal Society;
-it could be a transcendental number like <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-32-Frame" class="MathJax"><nobr><span id="MathJax-Span-1557" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.967em, 1000em, 2.763em, -0.507em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1558" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1559" class="mi">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.032em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.602em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-32" type="math/tex">\pi</script>. All that matters from
-our point of view is that we know how to map the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-33-Frame" class="MathJax"><nobr><span id="MathJax-Span-1560" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1561" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1562" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1563" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1565" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1566" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-33" type="math/tex">Thing</script> to its time interval and attribute mapping.
-</p>
-
-
-<p>It is possible for two Things to be indistinguishable by their attribute values and lifetime, but have different identity.
-</p>
-
-
-</section>
-
-<section id="objects-1">
-<h3><span class="secno">3.2 </span> Objects </h3>
-
-<p>
-An <em>Object</em> is described by a time interval and attributes with unchanging values. Objects encompass entities, interactions, and activities.
-To model this, a structure includes:
-</p>
-
-<div data-title="Component 2 (objects)" data-count="2" class="component" id="objects"><div class="ruleTitle"><a href="#objects" class="internalDFN">Component 2 (objects)</a></div>
- <ol><li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-34-Frame" class="MathJax"><nobr><span id="MathJax-Span-1567" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1568" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1569" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1570" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1571" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1572" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1573" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1575" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-34" type="math/tex">Objects</script>
-</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-35-Frame" class="MathJax"><nobr><span id="MathJax-Span-1576" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1577" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1578" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1579" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1580" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1581" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1582" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1583" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1584" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1585" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1586" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1587" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1588" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1589" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1591" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1592" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1593" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1594" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1595" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1596" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1598" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1599" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1600" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1601" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1602" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1603" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-35" type="math/tex">lifetime : Objects \to Intervals</script> from objects to time intervals
-</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-36-Frame" class="MathJax"><nobr><span id="MathJax-Span-1604" class="math"><span style="display: inline-block; position: relative; width: 291px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1605" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1606" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1607" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1608" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1609" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1610" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1611" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1612" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1613" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1614" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1615" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1616" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1618" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1619" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1620" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1621" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1622" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1623" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1624" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1625" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1626" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1628" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1629" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1630" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1631" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1632" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1633" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1634" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1635" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1636" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1637" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1638" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1639" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-36" type="math/tex">value : Objects \times Attributes \to P(Values)</script>
-</li></ol>
-</div>
-
-<p>Intuitively, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-37-Frame" class="MathJax"><nobr><span id="MathJax-Span-1640" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1641" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1642" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1643" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1644" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1645" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1646" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1647" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1648" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1649" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1650" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1651" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1652" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-37" type="math/tex">lifetime(e)</script> is the time interval during which object
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-38-Frame" class="MathJax"><nobr><span id="MathJax-Span-1653" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1654" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1655" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-38" type="math/tex">e</script> exists. The set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-39-Frame" class="MathJax"><nobr><span id="MathJax-Span-1656" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1657" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1658" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1660" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1662" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1663" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1664" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1665" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1666" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1667" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-39" type="math/tex">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-40-Frame" class="MathJax"><nobr><span id="MathJax-Span-1668" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1669" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1670" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-40" type="math/tex">a</script> during the object's lifetime.
-</p>
-
-<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-41-Frame" class="MathJax"><nobr><span id="MathJax-Span-1671" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1672" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1673" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1674" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1675" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1676" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1677" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-41" type="math/tex">value</script> is sets of values,
-making <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-42-Frame" class="MathJax"><nobr><span id="MathJax-Span-1678" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1679" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1680" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1681" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1682" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1683" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1684" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-42" type="math/tex">value</script> effectively a multivalued function. It is also possible to have two different objects that are indistinguishable by their attributes and time intervals. Objects are not things, and the sets of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-43-Frame" class="MathJax"><nobr><span id="MathJax-Span-1685" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1686" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1687" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1688" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1689" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1690" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1691" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1693" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-43" type="math/tex">Objects</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-44-Frame" class="MathJax"><nobr><span id="MathJax-Span-1694" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1695" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1696" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1697" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1698" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1699" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1700" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1701" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-44" type="math/tex">Things</script> are disjoint; however, certain objects, namely entities, are linked to things.
-
-</p>
-<section id="entities-1">
-<h4><span class="secno">3.2.1 </span> Entities </h4>
-
-An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:
-
-<div data-title="Component 3 (entities)" data-count="3" class="component" id="entities"><div class="ruleTitle"><a href="#entities" class="internalDFN">Component 3 (entities)</a></div>
- <ol><li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-45-Frame" class="MathJax"><nobr><span id="MathJax-Span-1702" class="math"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1703" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1704" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1705" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1706" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1707" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1709" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1710" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1711" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1712" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1713" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1714" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1715" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1717" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1719" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-45" type="math/tex">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-46-Frame" class="MathJax"><nobr><span id="MathJax-Span-1720" class="math"><span style="display: inline-block; position: relative; width: 64px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.763em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1721" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1722" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1723" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1725" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1726" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1728" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1729" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1730" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1731" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.859em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-46" type="math/tex">Activities</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-47-Frame" class="MathJax"><nobr><span id="MathJax-Span-1732" class="math"><span style="display: inline-block; position: relative; width: 46px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1733" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1734" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1735" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1736" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1737" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1739" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-47" type="math/tex">Events</script> below.
-</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-48-Frame" class="MathJax"><nobr><span id="MathJax-Span-1740" class="math"><span style="display: inline-block; position: relative; width: 199px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1741" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1742" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1743" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1744" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1745" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1746" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1747" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1748" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1749" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1750" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1751" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1753" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1754" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1755" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1757" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1758" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1759" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1760" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1762" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1763" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1764" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-48" type="math/tex">thingOf : Entities \to Things</script> that associates each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-49-Frame" class="MathJax"><nobr><span id="MathJax-Span-1765" class="math"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1766" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1767" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1768" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1772" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-49" type="math/tex">Entity</script> with a <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-50-Frame" class="MathJax"><nobr><span id="MathJax-Span-1773" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1774" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1775" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1776" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1778" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1779" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-50" type="math/tex">Thing</script>, such that for each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-51-Frame" class="MathJax"><nobr><span id="MathJax-Span-1780" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1781" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1783" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1784" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1785" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1786" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1787" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1789" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1790" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1791" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1792" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1793" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1794" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1795" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1796" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-51" type="math/tex">t \in lifetime(obj)</script>, and for each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-52-Frame" class="MathJax"><nobr><span id="MathJax-Span-1797" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1798" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1799" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-52" type="math/tex">a</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-53-Frame" class="MathJax"><nobr><span id="MathJax-Span-1800" class="math"><span style="display: inline-block; position: relative; width: 274px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1801" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1802" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1803" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1804" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1805" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1806" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1807" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1808" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1809" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1810" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1811" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1812" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1813" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1814" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1815" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1816" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1817" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1818" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1819" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1820" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1822" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1823" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1825" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1826" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1827" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1829" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1830" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1831" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1832" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1833" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1834" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1835" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1837" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-53" type="math/tex">value(obj,a) \subseteq value(thingOf(obj),a,t)</script>.
-</li><li> <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-54-Frame" class="MathJax"><nobr><span id="MathJax-Span-1838" class="math"><span style="display: inline-block; position: relative; width: 166px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1839" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1840" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1841" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1842" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1843" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1845" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1846" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1847" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1848" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1849" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1850" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1851" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1852" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1853" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1854" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1855" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1856" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1857" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1858" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1859" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1860" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1861" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1862" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-54" type="math/tex">lifetime(e) \subseteq lifetime(t)</script>.
-</li></ol>
-</div>
-
-<div class="remark"><p> Although both entities and things can have
- undefined or multiple attribute values, their meaning is slightly
- different: for a thing, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-55-Frame" class="MathJax"><nobr><span id="MathJax-Span-1863" class="math"><span style="display: inline-block; position: relative; width: 116px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1864" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1865" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1866" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1867" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1868" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1869" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1870" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1871" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1872" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1873" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1874" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1875" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1876" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1877" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1878" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-55" type="math/tex">value(x,a,t) = \emptyset</script> means that the
- attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-56-Frame" class="MathJax"><nobr><span id="MathJax-Span-1879" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1880" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1881" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-56" type="math/tex">a</script> has no value at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-57-Frame" class="MathJax"><nobr><span id="MathJax-Span-1882" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1883" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-57" type="math/tex">t</script>, whereas for an entity,
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-58-Frame" class="MathJax"><nobr><span id="MathJax-Span-1885" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1886" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1887" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1888" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1889" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1890" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1891" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1892" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1893" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1894" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1895" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1896" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1897" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1898" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-58" type="math/tex">value(x,a) = \emptyset</script> only means that the entity does not record
- a fixed value for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-59-Frame" class="MathJax"><nobr><span id="MathJax-Span-1899" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1900" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1901" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-59" type="math/tex">a</script> forthe associated thing. This does not imply
- that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-60-Frame" class="MathJax"><nobr><span id="MathJax-Span-1902" class="math"><span style="display: inline-block; position: relative; width: 182px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1904" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1905" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1906" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1907" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1908" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1909" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1910" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1911" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1912" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1913" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1914" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1915" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1916" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1917" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1918" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1919" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1920" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1921" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1922" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1923" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1924" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1925" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1926" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.127em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-60" type="math/tex">value(thingOf(e),a,t) = \emptyset</script> when <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-61-Frame" class="MathJax"><nobr><span id="MathJax-Span-1927" class="math"><span style="display: inline-block; position: relative; width: 100px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1928" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1930" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1931" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1932" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1933" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1934" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1935" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1936" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1937" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1938" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1939" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1940" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1941" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-61" type="math/tex">t \in lifetime(e)</script>.
-</p>
- <p>Furthermore, all of the attribute values of the entity must be
- present in the associated thing throughout the lifetime of the entity.
-For example, suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-62-Frame" class="MathJax"><nobr><span id="MathJax-Span-1942" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1943" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1944" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1945" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1946" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1947" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1948" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1949" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1950" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1951" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1952" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1953" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1954" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1955" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1956" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1957" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1958" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1959" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1961" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1962" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1963" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1964" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-62" type="math/tex">value(thingOf(e),a,t)</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-63-Frame" class="MathJax"><nobr><span id="MathJax-Span-1965" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1966" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1967" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1968" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1969" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-63" type="math/tex">\{1\}</script> at some
-time in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-64-Frame" class="MathJax"><nobr><span id="MathJax-Span-1970" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1971" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1972" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1973" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1974" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1975" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1976" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1978" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1979" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1980" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1981" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1982" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-64" type="math/tex">lifetime(e)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-65-Frame" class="MathJax"><nobr><span id="MathJax-Span-1983" class="math"><span style="display: inline-block; position: relative; width: 202px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.632em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1984" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1985" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1987" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1988" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1989" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1990" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1992" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1995" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1996" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1997" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1998" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1999" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2000" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2001" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2002" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2003" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-2004" class="msup"><span style="display: inline-block; position: relative; width: 0.656em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.466em; left: 0.347em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-2006" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2007" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2008" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2009" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2010" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2011" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.162em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-65" type="math/tex">value(thingOf(e),a,t') = \{2\}</script> at some
- other time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-66-Frame" class="MathJax"><nobr><span id="MathJax-Span-2012" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.107em, 1000em, 2.231em, -0.488em); top: -2.044em; left: 0em;"><span id="MathJax-Span-2013" class="mrow"><span id="MathJax-Span-2014" class="msup"><span style="display: inline-block; position: relative; width: 0.656em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.466em; left: 0.347em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-2016" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.953em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-66" type="math/tex">t'</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-67-Frame" class="MathJax"><nobr><span id="MathJax-Span-2017" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2018" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2019" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2021" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2022" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2023" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2024" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2025" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2027" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2028" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-67" type="math/tex">value(e,a)</script> must be <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-68-Frame" class="MathJax"><nobr><span id="MathJax-Span-2029" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.819em, -0.498em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2030" class="mrow"><span style="font-family: STIXVariants;" id="MathJax-Span-2031" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.984em; vertical-align: -0.142em;"></span></span></nobr></span><script id="MathJax-Element-68" type="math/tex">\emptyset</script> because
- there is no other set of values that is simultaneously contained in
- both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-69-Frame" class="MathJax"><nobr><span id="MathJax-Span-2032" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2033" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2034" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2035" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2036" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-69" type="math/tex">\{1\}</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-70-Frame" class="MathJax"><nobr><span id="MathJax-Span-2037" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2038" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2039" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2040" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2041" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-70" type="math/tex">\{2\}</script>.
-</p>
- </div>
-
-<section id="plans-1">
-<h5><span class="secno">3.2.1.1 </span> Plans </h5>
-<p>We identify a specific subset of the entities called
- <em>plans</em>:
-</p><div data-title="Component 4 (plans)" data-count="4" class="component" id="plans"><div class="ruleTitle"><a href="#plans" class="internalDFN">Component 4 (plans)</a></div>
- <p> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-71-Frame" class="MathJax"><nobr><span id="MathJax-Span-2042" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2043" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2044" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2045" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2046" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2047" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2048" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2049" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2050" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2051" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2053" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2054" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2055" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2056" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2057" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-71" type="math/tex">Plans \subseteq Entities</script> of plans.</p>
- </div>
-<p></p></section>
-
- </section>
-
- <section id="actvities">
-<h4><span class="secno">3.2.2 </span> Actvities </h4>
-
-
-<p>An <em>activity</em> is an object that encompasses a set of events. We introduce
-</p>
-<div data-title="Component 5 (activities)" data-count="5" class="component" id="activities"><div class="ruleTitle"><a href="#activities" class="internalDFN">Component 5 (activities)</a></div>
- <ol><li>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-72-Frame" class="MathJax"><nobr><span id="MathJax-Span-2058" class="math"><span style="display: inline-block; position: relative; width: 139px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2059" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2060" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2061" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2064" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2065" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2066" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2067" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2069" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2070" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2071" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2072" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2073" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2075" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2076" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2077" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-72" type="math/tex">Activities \subseteq Objects</script> of activities.</li>
- <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-73-Frame" class="MathJax"><nobr><span id="MathJax-Span-2078" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.819em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2079" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2080" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2081" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2082" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2085" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2086" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2087" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2088" class="mo">∩</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2089" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2090" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2091" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2092" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2093" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2094" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2096" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2097" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2098" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2099" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-2100" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.984em; vertical-align: -0.142em;"></span></span></nobr></span><script id="MathJax-Element-73" type="math/tex">Entities\cap Activities
- = \emptyset</script>.</li>
- </ol>
-</div></section>
-
- <section id="agents-1">
-<h4><span class="secno">3.2.3 </span> Agents </h4>
-
-<p>An agent is an object that can act, by controlling, starting,
- ending, or participating in activities. Agents can act on behalf of
- other agents. An agent can be an entity, an activity, or neither; an
- agent cannot be both entity and activity because the sets of
- entities and activities are disjoint. We introduce:
-</p>
-<div data-title="Component 6 (agents)" data-count="6" class="component" id="agents"><div class="ruleTitle"><a href="#agents" class="internalDFN">Component 6 (agents)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-74-Frame" class="MathJax"><nobr><span id="MathJax-Span-2101" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2102" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2103" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2104" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2105" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2106" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2108" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2109" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2110" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2111" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2112" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2113" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2114" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2116" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-74" type="math/tex">Agents \subseteq Objects</script> of agents.</p>
- </div>
-</section>
-
-
-<section id="interactions-1">
-<h4><span class="secno">3.2.4 </span> Interactions </h4>
-
-<p>We consider a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-75-Frame" class="MathJax"><nobr><span id="MathJax-Span-2117" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2118" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2119" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2120" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2121" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2123" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2124" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2125" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2126" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2127" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2129" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2130" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2131" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2132" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2133" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2134" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2135" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2136" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2137" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2138" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-75" type="math/tex">Interactions \subseteq Objects</script> which are split into
- <em>Events</em> connecting entities and activities,
- <em>Associations</em> between agents and activities,
- <em>Communications</em> between pairs of activities,
- <em>Delegations</em> between pairs of agents, and <em>Derivations</em> that describe chains of generation and usage steps. (The first two sets may overlap.) Interactions are disjoint from entities, activities and agents.
-</p>
-<div data-title="Component 7 (interactions)" data-count="7" class="component" id="interactions"><div class="ruleTitle"><a href="#interactions" class="internalDFN">Component 7 (interactions)</a></div>
- <ol><li> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-76-Frame" class="MathJax"><nobr><span id="MathJax-Span-2139" class="math"><span style="display: inline-block; position: relative; width: 672px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2141" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2142" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2143" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2145" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2146" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2147" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2149" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2150" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2151" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2152" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2153" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2154" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2155" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2156" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2157" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2159" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2160" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2161" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2162" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2163" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2164" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2165" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2166" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2167" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2168" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2169" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2170" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2171" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2172" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2173" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2174" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2175" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2176" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2177" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2178" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2179" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2180" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2181" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2183" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2184" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2185" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2186" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2187" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2188" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2189" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2190" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2191" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2193" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2194" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2197" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2198" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2199" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2200" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2201" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2203" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2204" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2205" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2208" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2209" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2210" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2211" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2212" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2213" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2214" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2215" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2216" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2217" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2218" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2219" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-76" type="math/tex">Interactions = Events \cup Associations \cup
- Communications \cup Delegations \cup Derivations \subseteq Objects</script>
-</li>
-<li> A function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-77-Frame" class="MathJax"><nobr><span id="MathJax-Span-2220" class="math"><span style="display: inline-block; position: relative; width: 939px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.954em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2221" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2222" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2223" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2224" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2225" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2226" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2227" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2228" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2230" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2231" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2232" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2233" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2236" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2237" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2238" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2239" class="mo">→</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2240" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2241" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2242" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2244" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2248" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2249" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2250" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2251" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2252" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2253" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2254" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2255" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2256" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2257" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2258" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2259" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2260" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2261" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2262" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2264" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2265" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2266" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2268" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2269" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2270" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2272" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2273" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2274" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2275" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2276" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2277" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2278" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2279" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2280" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2281" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2282" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2283" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2284" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2285" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2288" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2289" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2290" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2291" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2292" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2293" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2294" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2295" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2296" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2297" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2298" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2300" class="mi">q</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2301" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2303" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2304" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2306" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2307" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2308" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2309" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2310" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2312" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2313" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2315" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2316" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2317" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2318" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2319" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2320" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2321" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2322" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2324" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2325" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2326" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2327" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2328" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2329" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2330" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2331" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2332" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2333" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2334" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2335" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2336" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2338" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2339" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2340" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2341" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2342" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2343" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2344" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2345" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2346" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.079em; vertical-align: -0.286em;"></span></span></nobr></span><script id="MathJax-Element-77" type="math/tex">type: Interactions \to
- \{start,end,usage,generation,invalidation,derivation,version,quotation,primarySource,attribution,delegation\}</script>.
-</li>
-<li> The sets <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-78-Frame" class="MathJax"><nobr><span id="MathJax-Span-2347" class="math"><span style="display: inline-block; position: relative; width: 46px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2348" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2349" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2350" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2351" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2352" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2353" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2354" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-78" type="math/tex">Events</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-79-Frame" class="MathJax"><nobr><span id="MathJax-Span-2355" class="math"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2356" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2357" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2358" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2359" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2360" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2361" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2362" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2365" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2366" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2367" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2368" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-79" type="math/tex">Associations</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-80-Frame" class="MathJax"><nobr><span id="MathJax-Span-2369" class="math"><span style="display: inline-block; position: relative; width: 117px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.729em, 1000em, 2.763em, -0.46em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2370" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2371" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2372" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2373" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2374" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2375" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2376" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2377" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2378" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2379" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2380" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2381" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2382" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2383" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2384" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.857em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-80" type="math/tex">Communications</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-81-Frame" class="MathJax"><nobr><span id="MathJax-Span-2385" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2386" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2387" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2389" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2390" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2391" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2392" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2393" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2394" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2395" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2396" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2397" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-81" type="math/tex">Delegations</script>
- and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-82-Frame" class="MathJax"><nobr><span id="MathJax-Span-2398" class="math"><span style="display: inline-block; position: relative; width: 81px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.763em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2399" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2400" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2401" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2402" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2403" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2404" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2405" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2406" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2407" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2408" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2409" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2410" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.844em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-82" type="math/tex">Derivations</script> are all disjoint.
-</li><li> Interactions are disjoint from entities, agents and
-activities: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-83-Frame" class="MathJax"><nobr><span id="MathJax-Span-2411" class="math"><span style="display: inline-block; position: relative; width: 348px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.951em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2412" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2413" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2414" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2416" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2417" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2418" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2419" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2420" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2421" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2422" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2423" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2424" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2425" class="mo">∩</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2426" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2427" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2428" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2429" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2430" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2432" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2433" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2434" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2435" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2436" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2437" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2438" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2439" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2440" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2441" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2442" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2443" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2444" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2445" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2446" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2447" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2448" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2449" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2450" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2452" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2453" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2454" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-2455" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.125em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-83" type="math/tex">Interactions \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
-</li></ol>
-</div>
-
-<section id="events-1">
-<h5><span class="secno">3.2.4.1 </span> Events </h5>
-
-<p>An <em>Event</em> is an interaction whose lifetime is a single time
-instant, and relates an activity to an entity (which could be an
-agent). Events have types including usage, generation, invalidation, starting and ending. Events are instantaneous. We introduce:
-</p>
-<div data-title="Component 8 (events)" data-count="8" class="component" id="events"><div class="ruleTitle"><a href="#events" class="internalDFN">Component 8 (events)</a></div>
-<ol><li> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-84-Frame" class="MathJax"><nobr><span id="MathJax-Span-2456" class="math"><span style="display: inline-block; position: relative; width: 153px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2457" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2458" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2459" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2460" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2461" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2462" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2463" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2464" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2465" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2466" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2468" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2469" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2471" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2472" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2473" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2474" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2475" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2476" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.935em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-84" type="math/tex">Events \subseteq Interactions</script> of events, such that
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-85-Frame" class="MathJax"><nobr><span id="MathJax-Span-2477" class="math"><span style="display: inline-block; position: relative; width: 381px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2478" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2480" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2481" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2482" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2483" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2485" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2486" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2487" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2488" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2489" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2490" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2491" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2492" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2493" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2494" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2495" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2496" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2497" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2498" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2499" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2500" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2502" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2503" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2504" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2505" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2506" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2507" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2508" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2509" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2511" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2512" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2513" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2514" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2515" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2516" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2517" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2518" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2519" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2520" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2521" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2522" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2523" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2524" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2527" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2528" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2529" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-85" type="math/tex">type(evt) \in \{start,end,generation,usage,invalidation\}</script> if and
- only of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-86-Frame" class="MathJax"><nobr><span id="MathJax-Span-2530" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.772em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2531" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2532" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2533" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2535" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2536" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2537" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2538" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2539" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2541" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-86" type="math/tex">evt \in Events</script>.
-</li><li> A function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-87-Frame" class="MathJax"><nobr><span id="MathJax-Span-2542" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.763em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2543" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2546" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2547" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2548" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2549" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2550" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2551" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2552" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2554" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2555" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2556" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2557" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2558" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2559" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2560" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.844em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-87" type="math/tex">time : Events \to Times</script> giving the time of each event; i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-88-Frame" class="MathJax"><nobr><span id="MathJax-Span-2561" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2562" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2563" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2565" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2566" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2567" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2568" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2569" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2570" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2571" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2572" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2573" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2575" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2576" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2577" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2579" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2580" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2581" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2582" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2584" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2585" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-88" type="math/tex">lifetime(evt) = \{time(t)\}</script>.
-</li><li> The derived ordering on events given by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-89-Frame" class="MathJax"><nobr><span id="MathJax-Span-2586" class="math"><span style="display: inline-block; position: relative; width: 284px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2587" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2588" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2589" class="mi">v</span><span id="MathJax-Span-2590" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2591" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2592" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2593" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2595" class="mi">v</span><span id="MathJax-Span-2596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2598" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="height: 0em; vertical-align: 0em; width: 0.313em; display: inline-block; overflow: hidden;" id="MathJax-Span-2599" class="mspace"></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2600" class="mo">⟺</span><span style="height: 0em; vertical-align: 0em; width: 0.313em; display: inline-block; overflow: hidden;" id="MathJax-Span-2601" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2603" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2604" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2605" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2606" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2607" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2608" class="mi">v</span><span id="MathJax-Span-2609" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2610" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2611" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2612" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2613" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2614" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2615" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2616" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2617" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2618" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2620" class="mi">v</span><span id="MathJax-Span-2621" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2622" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2623" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2624" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-89" type="math/tex">evt_1 \leq evt_2 \iff time(evt_1) \leq time(evt_2)</script>
-</li></ol>
-</div>
-</section>
-<section id="associations-1">
-
-<h5><span class="secno">3.2.4.2 </span> Associations </h5>
-
-<p>An <em>Association</em> is an interaction relating an agent to an activity. To model associations, we introduce:
-</p>
-<div data-title="Component 9 (associations)" data-count="9" class="component" id="associations"><div class="ruleTitle"><a href="#associations" class="internalDFN">Component 9 (associations)</a></div>
- <p>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-90-Frame" class="MathJax"><nobr><span id="MathJax-Span-2625" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.848em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2626" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2627" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2628" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2629" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2630" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2631" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2632" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2633" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2634" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2635" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2636" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2637" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2638" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2639" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2640" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2641" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2642" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2643" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2644" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2645" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2647" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2648" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2649" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2650" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2651" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.95em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-90" type="math/tex">Associations \subseteq Interactions</script>, such that
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-91-Frame" class="MathJax"><nobr><span id="MathJax-Span-2652" class="math"><span style="display: inline-block; position: relative; width: 179px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2655" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2656" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2657" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2658" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2660" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2661" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2662" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2663" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2664" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2665" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2668" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2669" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2670" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2672" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2674" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2675" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2676" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-91" type="math/tex">type(assoc) = association</script> if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-92-Frame" class="MathJax"><nobr><span id="MathJax-Span-2677" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.772em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2678" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2680" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2681" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2682" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2683" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2684" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2685" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2686" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2687" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2688" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2689" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2690" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2691" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2693" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2694" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2695" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2696" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.869em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-92" type="math/tex">assoc \in Associations</script>.
-</p>
- </div>
-
-<p>Associations are used below in the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-93-Frame" class="MathJax"><nobr><span id="MathJax-Span-2697" class="math"><span style="display: inline-block; position: relative; width: 56px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2698" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2699" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2700" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2701" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2702" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2703" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2704" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2705" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-93" type="math/tex">ActsFor</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-94-Frame" class="MathJax"><nobr><span id="MathJax-Span-2706" class="math"><span style="display: inline-block; position: relative; width: 109px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2707" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2708" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2709" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2710" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2711" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2712" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2713" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2714" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2715" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2717" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2718" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2719" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2720" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2721" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-94" type="math/tex">AssociatedWith</script> relations.
-
-
-</p></section>
- <section id="communications">
- <h5><span class="secno">3.2.4.3 </span>Communications</h5>
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO</div></div>
-
-</section>
- <section id="delegations">
- <h5><span class="secno">3.2.4.4 </span>Delegations</h5>
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO</div></div>
-</section>
- <section id="derivations-1">
-
- <h5><span class="secno">3.2.4.5 </span> Derivations </h5>
-
-<p>A <em>Derivation</em> is an interaction chaining one or more generation and use steps.
-</p>
-<div data-title="Component 10 (derivations)" data-count="10" class="component" id="derivations"><div class="ruleTitle"><a href="#derivations" class="internalDFN">Component 10 (derivations)</a></div>
-<p> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-95-Frame" class="MathJax"><nobr><span id="MathJax-Span-2722" class="math"><span style="display: inline-block; position: relative; width: 188px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2723" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2724" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2725" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2726" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2728" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2729" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2730" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2731" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2732" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2733" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2734" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2735" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2736" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2737" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2740" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2741" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2742" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2743" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2744" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2745" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2746" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2747" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.935em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-95" type="math/tex">Derivations \subseteq Interactions</script>, such that
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-96-Frame" class="MathJax"><nobr><span id="MathJax-Span-2748" class="math"><span style="display: inline-block; position: relative; width: 427px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.954em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2749" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2750" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2751" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2752" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2753" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2754" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2755" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2757" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2758" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2759" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2760" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2761" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2762" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2763" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2764" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2765" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2766" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2767" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2768" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2771" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2772" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2773" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2774" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2775" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2776" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2777" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2778" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2779" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2780" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2781" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2782" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2783" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2784" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2785" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2786" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2787" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2788" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2789" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2790" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2791" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2792" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2793" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2794" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2795" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2796" class="mi">q</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2797" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2798" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2799" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2800" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2801" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2802" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2803" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2804" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2805" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.079em; vertical-align: -0.286em;"></span></span></nobr></span><script id="MathJax-Element-96" type="math/tex">type(deriv) \in \{derivation, version, primarySource,quotation\}</script>
- if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-97-Frame" class="MathJax"><nobr><span id="MathJax-Span-2806" class="math"><span style="display: inline-block; position: relative; width: 140px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.772em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2807" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2808" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2809" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2810" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2812" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2813" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2814" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2815" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2816" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2818" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2819" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2820" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2821" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2822" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2823" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2824" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.885em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-97" type="math/tex">deriv \in Derivations</script>.
-</p></div>
-<p>See below for the associated derivation path and DerivedFrom relation.
-</p>
-</section>
-</section>
-</section>
-<section id="relations">
-
-<h3><span class="secno">3.3 </span> Relations </h3>
-
-<h3 id="simple-relations"> Simple relations </h3>
-<p>The entities, interactions, and activities in a structure are related in the following ways:
-</p>
-<ol><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-98-Frame" class="MathJax"><nobr><span id="MathJax-Span-2825" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.424em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2826" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2827" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2828" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2829" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2830" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2831" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2832" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2833" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2834" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2835" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2837" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2838" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2839" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2840" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2841" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2844" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2845" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2846" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-98" type="math/tex">Used \subseteq Events \times Entities</script> saying when an event used an entity. An event can use at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-99-Frame" class="MathJax"><nobr><span id="MathJax-Span-2847" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2848" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2849" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2851" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2853" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2854" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2855" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2856" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2857" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2858" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2859" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2860" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-99" type="math/tex">(evt,e)\in Used</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-100-Frame" class="MathJax"><nobr><span id="MathJax-Span-2861" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2862" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2864" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2865" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2866" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2867" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2868" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2869" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2870" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2871" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2872" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2873" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2875" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2876" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2877" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2878" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2879" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2880" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2881" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2882" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2883" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-100" type="math/tex">time(evt) \in lifetime(e)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-101-Frame" class="MathJax"><nobr><span id="MathJax-Span-2884" class="math"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2885" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2886" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2887" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2888" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2889" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2890" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2891" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2892" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2893" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2894" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2895" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2896" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-101" type="math/tex">type(g) = use</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-102-Frame" class="MathJax"><nobr><span id="MathJax-Span-2897" class="math"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.474em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2898" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2899" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2900" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2901" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2902" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2903" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2904" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2905" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2906" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2907" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2908" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2909" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2910" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2911" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2912" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2914" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2915" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2916" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2917" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2918" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2919" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2920" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2921" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2922" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2923" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-102" type="math/tex">Generated \subseteq Events \times Entities</script> saying when an event generated an entity. An event can generate at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-103-Frame" class="MathJax"><nobr><span id="MathJax-Span-2924" class="math"><span style="display: inline-block; position: relative; width: 143px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2925" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2926" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2927" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2928" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2930" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2931" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2932" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2933" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2934" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2935" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2936" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2939" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2941" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2942" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-103" type="math/tex">(evt,e)\in Generated</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-104-Frame" class="MathJax"><nobr><span id="MathJax-Span-2943" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2944" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2945" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2946" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2947" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2948" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2949" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2950" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2951" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2952" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2954" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2955" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2956" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2957" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2958" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2959" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2960" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2961" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2962" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2963" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2964" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2965" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2966" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2967" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2968" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2969" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2970" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-104" type="math/tex">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-105-Frame" class="MathJax"><nobr><span id="MathJax-Span-2971" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2972" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2973" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2974" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2975" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2976" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2977" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2978" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2979" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2980" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2981" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2982" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2983" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2984" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2987" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2988" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2989" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2990" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-105" type="math/tex">type(g) = generation</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-106-Frame" class="MathJax"><nobr><span id="MathJax-Span-2991" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2992" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2993" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2995" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2996" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2997" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2998" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3000" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3001" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3002" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3003" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3004" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3005" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3006" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3007" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3008" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3010" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3011" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3012" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3013" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3017" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3018" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3019" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-106" type="math/tex">Invalidated \subseteq Events \times Entities</script> saying when an event invalidated an entity. An event can invalidate at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-107-Frame" class="MathJax"><nobr><span id="MathJax-Span-3020" class="math"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3021" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3022" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3023" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3024" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3025" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3027" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3028" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3029" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3030" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3031" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3032" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3033" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3034" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3035" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3036" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3037" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3039" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3040" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-107" type="math/tex">(evt,e)\in Invalidated</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-108-Frame" class="MathJax"><nobr><span id="MathJax-Span-3041" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3042" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3043" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3044" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3045" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3046" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3047" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3048" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3049" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3050" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3051" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3052" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3053" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3054" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3055" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3056" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3057" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3058" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3059" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3061" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3062" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3063" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3064" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3066" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3068" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-108" type="math/tex">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-109-Frame" class="MathJax"><nobr><span id="MathJax-Span-3069" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3070" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3071" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3072" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3073" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3074" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3075" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3076" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3077" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3078" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3079" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3080" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3081" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3082" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3083" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3084" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3085" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3086" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3087" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3088" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3089" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3090" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-109" type="math/tex">type(g) = invalidation</script> must hold.
-</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-110-Frame" class="MathJax"><nobr><span id="MathJax-Span-3091" class="math"><span style="display: inline-block; position: relative; width: 245px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.951em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3092" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3093" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3094" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3095" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3096" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3097" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3098" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3099" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3100" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3102" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3103" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3104" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3105" class="mi">y</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3106" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3107" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3108" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3109" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3110" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3111" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3112" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3113" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3114" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3115" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3117" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3118" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3119" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3123" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.06em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-110" type="math/tex">EventActivity \subseteq Events \times Activities</script> associating activities with events, such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-111-Frame" class="MathJax"><nobr><span id="MathJax-Span-3124" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3125" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3126" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3127" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3128" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3130" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3131" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3132" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3134" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3135" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3136" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3137" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3138" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3139" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3141" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3142" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3143" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3144" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3145" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3146" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3147" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3148" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-111" type="math/tex">(act,evt) \in EventActivity</script> implies <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-112-Frame" class="MathJax"><nobr><span id="MathJax-Span-3149" class="math"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3150" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3152" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3153" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3154" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3155" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3156" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3157" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3159" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3160" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3161" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3162" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3163" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3164" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3165" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3166" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3167" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3168" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3169" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3171" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3173" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-112" type="math/tex">time(evt) \in lifetime(act)</script>.
-</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-113-Frame" class="MathJax"><nobr><span id="MathJax-Span-3174" class="math"><span style="display: inline-block; position: relative; width: 430px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3175" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3176" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3177" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3178" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3179" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3180" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3181" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3183" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3184" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3185" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3186" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3187" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3188" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3189" class="mi">h</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3190" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3191" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3192" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3193" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3194" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3195" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3197" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3199" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3200" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3201" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3202" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3203" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3204" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3205" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3206" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3208" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3209" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3210" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3211" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3213" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3214" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3215" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3217" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3218" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3219" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3220" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3221" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3222" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3223" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3224" class="mi">n</span><span id="MathJax-Span-3225" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3226" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3227" class="mi">⊥</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-113" type="math/tex">AssociatedWith \subseteq Association \times Agents \times Activities \times Plans_\bot</script> indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan.
-</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-114-Frame" class="MathJax"><nobr><span id="MathJax-Span-3228" class="math"><span style="display: inline-block; position: relative; width: 377px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3229" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3230" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3231" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3232" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3233" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3234" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3235" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3236" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3237" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3238" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3239" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3240" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3241" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3242" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3246" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3247" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3248" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3249" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3250" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3251" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3252" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3253" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3255" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3256" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3257" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3258" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3259" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3260" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3262" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3263" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3264" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3265" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3267" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3268" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3269" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3271" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3272" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3273" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-114" type="math/tex">ActsFor \subseteq Delegations \times Agents \times Agents \times Activities</script> indicating when one agent acts on behalf of another with respect to a given activity.
-</li></ol>
-
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">
- TODO: Communication, start, end relations
- </div></div>
-
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">
- TODO: Specialization relation
- </div></div>
-
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">
- TODO: Explicit axioms concerning the relations
- </div></div>
-
-
-<section id="derivation-paths-and-derivedfrom">
-<h4><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </h4>
-
-<p>Recall that above we introduced a subset of interactions called <em>Derivations</em>. These identify <em>paths</em> of the form </p>
-
-<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-115-Frame" class="MathJax"><nobr><span id="MathJax-Span-3274" class="math"><span style="display: inline-block; position: relative; width: 388px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.993em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3275" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3276" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3277" class="mi">n</span><span id="MathJax-Span-3278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3280" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3281" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3283" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3284" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3285" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3287" class="mi">c</span><span id="MathJax-Span-3288" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3289" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3290" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3291" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3292" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3293" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3294" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3295" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3296" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3297" class="mi">n</span><span id="MathJax-Span-3298" class="msubsup"><span style="display: inline-block; position: relative; width: 1.517em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3299" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span id="MathJax-Span-3300" class="texatom"><span id="MathJax-Span-3301" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3302" class="mi">n</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3303" class="mo">−</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3304" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3305" class="mo">⋅</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3306" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3307" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3308" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3309" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3311" class="mi">n</span><span id="MathJax-Span-3312" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3314" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3315" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3316" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3317" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3318" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3319" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3321" class="mi">c</span><span id="MathJax-Span-3322" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3324" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3325" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3326" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3327" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3328" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3329" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3330" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3331" class="mi">n</span><span id="MathJax-Span-3332" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3333" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3334" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.974em; vertical-align: -0.328em;"></span></span></nobr></span></div><script id="MathJax-Element-115" type="math/tex; mode=display">ent_n\cdot g_n\cdot act_n\cdot u_n\cdot ent_{n-1}\cdot ...\cdot
-ent_1\cdot g_1\cdot act_1\cdot u_1\cdot ent_0</script>
-
-<p>where the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-116-Frame" class="MathJax"><nobr><span id="MathJax-Span-3335" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3336" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3338" class="mi">n</span><span id="MathJax-Span-3339" class="msubsup"><span style="display: inline-block; position: relative; width: 0.524em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3340" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3341" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-116" type="math/tex">ent_i</script> are entities, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-117-Frame" class="MathJax"><nobr><span id="MathJax-Span-3342" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3343" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3344" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3345" class="mi">c</span><span id="MathJax-Span-3346" class="msubsup"><span style="display: inline-block; position: relative; width: 0.524em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3348" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-117" type="math/tex">act_i</script> are activities, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-118-Frame" class="MathJax"><nobr><span id="MathJax-Span-3349" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.469em, -0.518em); top: -2.044em; left: 0em;"><span id="MathJax-Span-3350" class="mrow"><span id="MathJax-Span-3351" class="msubsup"><span style="display: inline-block; position: relative; width: 0.776em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3352" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3353" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.863em; vertical-align: -0.329em;"></span></span></nobr></span><script id="MathJax-Element-118" type="math/tex">g_i</script> are generations, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-119-Frame" class="MathJax"><nobr><span id="MathJax-Span-3354" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.377em, -0.484em); top: -2.044em; left: 0em;"><span id="MathJax-Span-3355" class="mrow"><span id="MathJax-Span-3356" class="msubsup"><span style="display: inline-block; position: relative; width: 0.776em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3357" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3358" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.766em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-119" type="math/tex">u_i</script> are usages.
-</p>
-<p>Formally, we consider the (regular) language:
-</p>
-<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-120-Frame" class="MathJax"><nobr><span id="MathJax-Span-3359" class="math"><span style="display: inline-block; position: relative; width: 473px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.595em, 1000em, 2.922em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3360" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3361" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3362" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3363" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3364" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3365" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3366" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3367" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3368" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3369" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3370" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3371" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3372" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3373" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3374" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3375" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3376" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3377" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3378" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3379" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3380" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3381" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3382" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3383" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3384" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3385" class="mo">⋅</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3386" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3387" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3388" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3389" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3390" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3392" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3393" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3394" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3395" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3397" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3398" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3399" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3400" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3401" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3402" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3403" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3404" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3405" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3406" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3408" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3409" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3410" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3411" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3412" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3413" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3415" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3416" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3417" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3418" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3419" class="mi">s</span><span id="MathJax-Span-3420" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.497em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-3421" class="mo">)</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.516em; left: 0.35em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3422" class="mo">+</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.17em; vertical-align: -0.252em;"></span></span></nobr></span></div><script id="MathJax-Element-120" type="math/tex; mode=display">DerivationPaths = Entities \cdot (Events \cdot Activities \cdot
-Events \cdot Entities)^+</script>
-<p>with the constraints that for each derivation path:
-</p>
-<ul>
-<li>for each substring <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-121-Frame" class="MathJax"><nobr><span id="MathJax-Span-3423" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3424" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3425" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3426" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3428" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3429" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3430" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3431" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3432" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3433" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-121" type="math/tex">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-122-Frame" class="MathJax"><nobr><span id="MathJax-Span-3434" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3435" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3436" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3437" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3438" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3439" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3440" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3441" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3442" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3443" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3444" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3445" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3446" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3447" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3448" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3449" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3451" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3452" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-122" type="math/tex">(g,ent) \in Generated</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-123-Frame" class="MathJax"><nobr><span id="MathJax-Span-3453" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3454" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3455" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3456" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3457" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3459" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3460" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3461" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3462" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3463" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3464" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3465" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3466" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3468" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3469" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3470" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3471" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3472" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3473" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3475" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3476" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3477" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-123" type="math/tex">(g,act) \in EventActivities</script>, and
-</li>
-<li>for each substring <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-124-Frame" class="MathJax"><nobr><span id="MathJax-Span-3478" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3479" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3480" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3481" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3483" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3484" class="mi">u</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3485" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3486" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3487" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-124" type="math/tex">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-125-Frame" class="MathJax"><nobr><span id="MathJax-Span-3489" class="math"><span style="display: inline-block; position: relative; width: 107px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3490" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3491" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3492" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3493" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3494" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3495" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3496" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3497" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3498" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3499" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3500" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3502" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-125" type="math/tex">(u,ent) \in Used</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-126-Frame" class="MathJax"><nobr><span id="MathJax-Span-3503" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3504" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3505" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3506" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3507" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3509" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3511" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3512" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3513" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3514" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3515" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3516" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3517" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3518" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3519" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3520" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3521" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3522" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3523" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3525" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3526" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3527" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-126" type="math/tex">(u,act) \in EventActivities</script>.
-</li>
-</ul>
-<p>We also consider a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-127-Frame" class="MathJax"><nobr><span id="MathJax-Span-3528" class="math"><span style="display: inline-block; position: relative; width: 329px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3529" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3530" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3531" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3532" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3533" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3534" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3535" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3536" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3537" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3539" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3540" class="mi">m</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3541" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3542" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3543" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3544" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3546" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3547" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3549" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3550" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3551" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3552" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3553" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3554" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3555" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3556" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3557" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3558" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3560" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3561" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3562" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3563" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3564" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3565" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3566" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3567" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3568" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-127" type="math/tex">derivedFrom : Derivations \to
-DerivationPaths</script> linking each derivation to its path.</p>
-
-
-<div class="remark">The reason why we need paths and not just individual derivation steps is that imprecise wasDerivedFrom formulas can represent multiple derivation steps.</div>
-</section>
-</section>
-
-<section id="putting-it-all-together">
-<h3><span class="secno">3.4 </span> Putting it all together </h3>
-
-<p>A <em>structure</em> <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-128-Frame" class="MathJax"><nobr><span id="MathJax-Span-3569" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3570" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3571" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-128" type="math/tex">W</script> is a structure containing all of the above
-described data. If we need to talk about the objects or relations of
-more than one structure then we may write <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-129-Frame" class="MathJax"><nobr><span id="MathJax-Span-3572" class="math"><span style="display: inline-block; position: relative; width: 82px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3573" class="mrow"><span id="MathJax-Span-3574" class="msubsup"><span style="display: inline-block; position: relative; width: 1.287em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3575" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.862em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3576" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3577" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3578" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3579" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3580" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3581" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3582" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3584" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-129" type="math/tex">W_1.Objects</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-130-Frame" class="MathJax"><nobr><span id="MathJax-Span-3585" class="math"><span style="display: inline-block; position: relative; width: 77px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3586" class="mrow"><span id="MathJax-Span-3587" class="msubsup"><span style="display: inline-block; position: relative; width: 1.287em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3588" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.862em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3589" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3590" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3591" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3592" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3593" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3594" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3595" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3596" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-130" type="math/tex">W_1.Things</script>,
-etc.; otherwise, to
-decrease notational clutter, when we consider a fixed structure then the names of the sets, relations and functions above refer to the components of that model.
-</p>
-
-</section>
-<section id="interpretations">
-<h3><span class="secno">3.5 </span> Interpretations </h3>
-
-<p>We need to link identifiers to the objects they denote. We do this using a function which we shall call an <em>interpretation</em>.
- Thus, we consider interpretations as follows:
-An interpretation is a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-131-Frame" class="MathJax"><nobr><span id="MathJax-Span-3597" class="math"><span style="display: inline-block; position: relative; width: 179px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3598" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3599" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3600" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3601" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3602" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3603" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3604" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3606" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3607" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3608" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3610" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3611" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3612" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3613" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3614" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3615" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3616" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3617" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3619" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-131" type="math/tex">\rho : Identifiers \to Objects</script> describing
-which object is the target of each identifier. The mapping from identifiers to objects may <b>not</b> change over time.
-</p>
-</section>
-
-</section>
-<section id="semantics">
-<!--OddPage--><h2><span class="secno">4. </span> Semantics </h2>
-
-<p>In what follows, let <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-132-Frame" class="MathJax"><nobr><span id="MathJax-Span-3620" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3621" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3622" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-132" type="math/tex">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-133-Frame" class="MathJax"><nobr><span id="MathJax-Span-3623" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3624" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3625" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-133" type="math/tex">I</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-134-Frame" class="MathJax"><nobr><span id="MathJax-Span-3626" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3627" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3628" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-134" type="math/tex">W</script>.
-The annotations [WF] refer to well-formedness constraints that correspond to typing constraints.
-</p>
-
-<section id="satisfaction">
-<h3><span class="secno">4.1 </span> Satisfaction </h3>
-
-<p>Consider a formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-135-Frame" class="MathJax"><nobr><span id="MathJax-Span-3629" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3630" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3631" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-135" type="math/tex">\phi</script>, a structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-136-Frame" class="MathJax"><nobr><span id="MathJax-Span-3632" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3633" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3634" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-136" type="math/tex">W</script> and an interpretation
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-137-Frame" class="MathJax"><nobr><span id="MathJax-Span-3635" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3636" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3637" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-137" type="math/tex">I</script>.
-We define notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-138-Frame" class="MathJax"><nobr><span id="MathJax-Span-3638" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3639" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3640" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3641" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3642" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3643" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3644" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-138" type="math/tex">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-139-Frame" class="MathJax"><nobr><span id="MathJax-Span-3645" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3646" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3647" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-139" type="math/tex">\phi</script> is
- satisfied in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-140-Frame" class="MathJax"><nobr><span id="MathJax-Span-3648" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3649" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3650" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3651" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3652" class="mi">ρ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.043em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-140" type="math/tex">W,\rho</script>. For atomic formulas, the definition of the
- satisfaction relation is given in the next few subsections. We give
- the standard definition of the semantics of the other formulas:
-</p>
-
-<div data-title="Formalism 11 (first-order-logic)" data-count="11" class="formalism" id="first-order-logic"><div class="ruleTitle"><a href="#first-order-logic" class="internalDFN">Formalism 11 (first-order-logic)</a></div>
-<ol>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-141-Frame" class="MathJax"><nobr><span id="MathJax-Span-3653" class="math"><span style="display: inline-block; position: relative; width: 88px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3654" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3655" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3657" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3658" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3659" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3662" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-141" type="math/tex">W,\rho \models True</script> always holds.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-142-Frame" class="MathJax"><nobr><span id="MathJax-Span-3663" class="math"><span style="display: inline-block; position: relative; width: 93px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3664" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3665" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3666" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3667" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3668" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3669" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3670" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3671" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3672" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3673" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-142" type="math/tex">W,\rho \models False</script> never holds.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-143-Frame" class="MathJax"><nobr><span id="MathJax-Span-3674" class="math"><span style="display: inline-block; position: relative; width: 76px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3675" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3676" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3677" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3678" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3679" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3680" class="mi">¬</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3681" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-143" type="math/tex">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-144-Frame" class="MathJax"><nobr><span id="MathJax-Span-3682" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3683" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3684" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3685" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3686" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3687" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3688" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-144" type="math/tex">W,\rho \models
- \phi</script> does not hold.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-145-Frame" class="MathJax"><nobr><span id="MathJax-Span-3689" class="math"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3690" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3691" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3693" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3694" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3695" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3696" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3697" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-145" type="math/tex">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-146-Frame" class="MathJax"><nobr><span id="MathJax-Span-3698" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3699" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3700" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3701" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3702" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3703" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3704" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-146" type="math/tex">W,\rho \models
- \phi</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-147-Frame" class="MathJax"><nobr><span id="MathJax-Span-3705" class="math"><span style="display: inline-block; position: relative; width: 62px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3706" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3707" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3708" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3709" class="mi">i</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3710" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3711" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-147" type="math/tex">W,i\models \psi</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-148-Frame" class="MathJax"><nobr><span id="MathJax-Span-3712" class="math"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3713" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3714" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3715" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3716" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3717" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3718" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3719" class="mo">∨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3720" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-148" type="math/tex">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-149-Frame" class="MathJax"><nobr><span id="MathJax-Span-3721" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3722" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3723" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3724" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3725" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3726" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3727" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-149" type="math/tex">W,\rho \models \phi</script>
- or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-150-Frame" class="MathJax"><nobr><span id="MathJax-Span-3728" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3729" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3730" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3731" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3732" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3733" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3734" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-150" type="math/tex">W,\rho \models \psi</script> holds.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-151-Frame" class="MathJax"><nobr><span id="MathJax-Span-3735" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3737" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3738" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3739" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3740" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3741" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3742" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3743" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-151" type="math/tex">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-152-Frame" class="MathJax"><nobr><span id="MathJax-Span-3744" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3745" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3746" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3747" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3748" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3749" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3750" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-152" type="math/tex">W,\rho \models \phi</script>
- implies <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-153-Frame" class="MathJax"><nobr><span id="MathJax-Span-3751" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3752" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3753" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3754" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3755" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3756" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3757" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-153" type="math/tex">W,\rho \models \psi</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-154-Frame" class="MathJax"><nobr><span id="MathJax-Span-3758" class="math"><span style="display: inline-block; position: relative; width: 90px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3759" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3760" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3761" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3762" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3763" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3764" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3765" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3766" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3767" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-154" type="math/tex">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-155-Frame" class="MathJax"><nobr><span id="MathJax-Span-3768" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3769" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3770" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3771" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3772" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3773" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3774" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3775" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3776" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3778" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3780" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-155" type="math/tex">obj \in
- Objects</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-156-Frame" class="MathJax"><nobr><span id="MathJax-Span-3781" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3782" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3783" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3785" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3786" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3787" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3788" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3789" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3790" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3791" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3792" class="mo">]</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3793" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3794" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-156" type="math/tex">W,\rho[x:=obj] \models \phi</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-157-Frame" class="MathJax"><nobr><span id="MathJax-Span-3795" class="math"><span style="display: inline-block; position: relative; width: 90px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3796" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3797" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3798" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3799" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3800" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3801" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3802" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3803" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3804" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-157" type="math/tex">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-158-Frame" class="MathJax"><nobr><span id="MathJax-Span-3805" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3806" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3807" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3808" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3809" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3810" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3811" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3812" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3813" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3814" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3815" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3817" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-158" type="math/tex">obj \in
- Objects</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-159-Frame" class="MathJax"><nobr><span id="MathJax-Span-3818" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3819" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3820" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3821" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3822" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3823" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3824" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3825" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3826" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3827" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3828" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3829" class="mo">]</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3830" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3831" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-159" type="math/tex">W,\rho[x:=obj] \models \phi</script>.</li>
- </ol></div>
-
-<div class="remark">
- <p>In the semantics above, note that the domain of quantification is
- the set of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-160-Frame" class="MathJax"><nobr><span id="MathJax-Span-3832" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3833" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3834" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3835" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3836" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3837" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3838" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3840" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-160" type="math/tex">Objects</script>; that is, quantifiers range over entities,
- activities, agents, or interactions (which are in turn further
- subdivided into types of interactions). <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-161-Frame" class="MathJax"><nobr><span id="MathJax-Span-3841" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3842" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3843" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3844" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3845" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3846" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3847" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3848" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-161" type="math/tex">Things</script> and relations
- cannot be referenced directly by identifiers.
-</p>
- </div>
-
- <div class="remark">
- <p>A PROV instance <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-162-Frame" class="MathJax"><nobr><span id="MathJax-Span-3849" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3850" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3851" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-162" type="math/tex">I</script> consists of a set of statements, each of
- which can be translated to an atomic formula following the
- definitional rules in PROV-CONSTRAINTS, possibly by introducing
- fresh existential variables. Thus, we can view an
- instance <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-163-Frame" class="MathJax"><nobr><span id="MathJax-Span-3852" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3853" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3854" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-163" type="math/tex">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-164-Frame" class="MathJax"><nobr><span id="MathJax-Span-3855" class="math"><span style="display: inline-block; position: relative; width: 84px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.992em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3856" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3857" class="mo">{</span><span id="MathJax-Span-3858" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3859" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3860" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3861" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3862" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3863" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3864" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3865" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3866" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3867" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.12em; vertical-align: -0.326em;"></span></span></nobr></span><script id="MathJax-Element-164" type="math/tex">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
- single formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-165-Frame" class="MathJax"><nobr><span id="MathJax-Span-3868" class="math"><span style="display: inline-block; position: relative; width: 176px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.992em, -0.453em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3869" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3870" class="mi">∃</span><span id="MathJax-Span-3871" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3872" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3873" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3874" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3875" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3876" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3877" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3878" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3879" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3880" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3881" class="mtext"> </span><span id="MathJax-Span-3882" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3883" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3884" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3885" class="mo">∧</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3886" class="mo">⋯</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3887" class="mo">∧</span><span style="padding-left: 0.25em;" id="MathJax-Span-3888" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3889" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3890" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.12em; vertical-align: -0.326em;"></span></span></nobr></span><script id="MathJax-Element-165" type="math/tex">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
- \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-166-Frame" class="MathJax"><nobr><span id="MathJax-Span-3891" class="math"><span style="display: inline-block; position: relative; width: 64px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.903em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3892" class="mrow"><span id="MathJax-Span-3893" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3894" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3895" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3896" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3897" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3898" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3899" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3900" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3901" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.766em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-166" type="math/tex">x_1,\ldots,x_k</script> are the existential
- variables of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-167-Frame" class="MathJax"><nobr><span id="MathJax-Span-3902" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3904" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-167" type="math/tex">I</script>.
- </p>
- </div>
-
-</section>
- <section id="attribute-matching">
-
-<h3><span class="secno">4.2 </span> Attribute matching </h3>
-
-
-<p>We say that an object <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-168-Frame" class="MathJax"><nobr><span id="MathJax-Span-3905" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3906" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3907" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3908" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3909" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-168" type="math/tex">obj</script> matches attributes <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-169-Frame" class="MathJax"><nobr><span id="MathJax-Span-3910" class="math"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.901em, -0.438em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3911" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3912" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3913" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3914" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3915" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3916" class="msubsup"><span style="display: inline-block; position: relative; width: 0.811em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3917" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3918" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3919" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3920" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3921" class="mi">a</span><span id="MathJax-Span-3922" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3923" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3924" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3925" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3926" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3927" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3928" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3929" class="mo">]</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.023em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-169" type="math/tex">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-170-Frame" class="MathJax"><nobr><span id="MathJax-Span-3930" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3931" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3932" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-170" type="math/tex">W</script> provided:
-for each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-171-Frame" class="MathJax"><nobr><span id="MathJax-Span-3933" class="math"><span style="display: inline-block; position: relative; width: 30px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3934" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3935" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3936" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3938" class="msubsup"><span style="display: inline-block; position: relative; width: 0.636em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3939" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3940" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-171" type="math/tex">attr_i</script>, we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-172-Frame" class="MathJax"><nobr><span id="MathJax-Span-3941" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3942" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3943" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3944" class="mi">a</span><span id="MathJax-Span-3945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.541em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3946" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3947" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3948" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3949" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3950" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3951" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3952" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3953" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3954" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3955" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3956" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3957" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3958" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3959" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3961" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3962" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3963" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3964" class="msubsup"><span style="display: inline-block; position: relative; width: 0.636em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3965" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3966" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3967" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-172" type="math/tex">val_i \in W.value(obj,attr_i)</script>.
-This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-173-Frame" class="MathJax"><nobr><span id="MathJax-Span-3968" class="math"><span style="display: inline-block; position: relative; width: 138px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3969" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3970" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3971" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3972" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3973" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3974" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3975" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3976" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3977" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3978" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3979" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3980" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3981" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3984" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3986" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3987" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-173" type="math/tex">match(W,obj,attrs)</script>.
-</p>
-
-</section>
-
-<section id="semantics-of-element-formulas">
-<h3><span class="secno">4.3 </span> Semantics of Element Formulas </h3>
-
-<section id="entity">
-
-<h4><span class="secno">4.3.1 </span> Entity </h4>
-
-<p>An entity formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-174-Frame" class="MathJax"><nobr><span id="MathJax-Span-3988" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3989" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3990" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3991" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3994" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3995" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3996" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3997" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3998" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3999" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4000" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4001" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4002" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4003" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4004" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4005" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-174" type="math/tex">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-175-Frame" class="MathJax"><nobr><span id="MathJax-Span-4006" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4007" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4008" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4009" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-175" type="math/tex">id</script> denotes an entity.
-</p>
-<p>Entity formulas <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-176-Frame" class="MathJax"><nobr><span id="MathJax-Span-4010" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4011" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4012" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4013" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4017" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4018" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4019" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4020" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4023" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4025" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4026" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4027" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-176" type="math/tex">entity(id,attrs)</script> can be interpreted as follows:
-</p>
-<div data-title="Formalism 12 (rule_12)" data-count="12" id="rule_12" class="formalism"><div class="ruleTitle"><a href="#rule_12" class="internalDFN">Formalism 12 (rule_12)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-177-Frame" class="MathJax"><nobr><span id="MathJax-Span-4028" class="math"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4029" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4030" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4031" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4032" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4033" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4034" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4035" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4036" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4037" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4039" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4040" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4042" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4043" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4044" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4046" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4047" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4048" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4049" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-177" type="math/tex">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-178-Frame" class="MathJax"><nobr><span id="MathJax-Span-4050" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4051" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4052" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4053" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-178" type="math/tex">id</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-179-Frame" class="MathJax"><nobr><span id="MathJax-Span-4054" class="math"><span style="display: inline-block; position: relative; width: 153px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4055" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4056" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4057" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4058" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4059" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4060" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4061" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4062" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4063" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4064" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4065" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4066" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4067" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4068" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4069" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4070" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4073" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-179" type="math/tex">ent = \rho(id) \in Entities</script>
-</li>
-<li>the attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-180-Frame" class="MathJax"><nobr><span id="MathJax-Span-4074" class="math"><span style="display: inline-block; position: relative; width: 137px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4075" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4076" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4078" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4079" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4080" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4081" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4082" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4083" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4084" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4085" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4086" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4087" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4088" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4089" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4091" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4092" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4093" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-180" type="math/tex">match(W,ent, attrs)</script>.
-</li>
-</ol>
-
-
-</div>
-<div class="remark">
-<p>For example, the following formulas all hold if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-181-Frame" class="MathJax"><nobr><span id="MathJax-Span-4094" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4095" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4096" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-181" type="math/tex">x</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-182-Frame" class="MathJax"><nobr><span id="MathJax-Span-4097" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4098" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4099" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-182" type="math/tex">e</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-183-Frame" class="MathJax"><nobr><span id="MathJax-Span-4100" class="math"><span style="display: inline-block; position: relative; width: 256px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.707em, 1000em, 2.926em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4101" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4102" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4103" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4104" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4105" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4106" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4107" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4108" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4109" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4110" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4111" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4112" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4113" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4114" class="mn">4</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4115" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-4116" class="mn">5</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4117" class="mo">}</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4118" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4119" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4120" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4121" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4122" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4123" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4124" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4125" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4126" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4127" class="mi">b</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4128" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4129" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4130" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4131" class="mn">6</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4132" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.055em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-183" type="math/tex">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
-</p><pre> entity(x,[])
- entity(x,[a=5])
- entity(x,[a=4,a=5])
- entity(x,[a=4,b=6])
-</pre>
-<p>Note that PROV-CONSTRAINTS normalization will merge these formulas
-to a single one:
-</p>
-<pre> entity(x,[a=4,a=5,b=6])
-</pre>
- </div>
-
- </section>
-<section id="activity">
-
-<h4><span class="secno">4.3.2 </span> Activity </h4>
-
-<p>An activity formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-184-Frame" class="MathJax"><nobr><span id="MathJax-Span-4133" class="math"><span style="display: inline-block; position: relative; width: 155px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4134" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4135" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4136" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4137" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4138" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4139" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4140" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4141" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4142" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4143" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4144" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4145" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4146" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4147" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4149" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4150" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4152" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4153" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4154" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4155" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4156" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4157" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4158" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-184" type="math/tex">activity(id,st,et,attrs)</script>
-where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-185-Frame" class="MathJax"><nobr><span id="MathJax-Span-4159" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4160" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4161" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4162" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-185" type="math/tex">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-186-Frame" class="MathJax"><nobr><span id="MathJax-Span-4163" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4164" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4165" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4166" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-186" type="math/tex">st</script> is a start
-time and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-187-Frame" class="MathJax"><nobr><span id="MathJax-Span-4167" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4168" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4169" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-187" type="math/tex">et</script> is an end time, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-188-Frame" class="MathJax"><nobr><span id="MathJax-Span-4171" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4172" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4175" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4176" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4177" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-188" type="math/tex">attrs</script> are the attributes of
-activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-189-Frame" class="MathJax"><nobr><span id="MathJax-Span-4178" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4179" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4180" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4181" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-189" type="math/tex">id</script>.
-</p>
-<div data-title="Formalism 13 (rule_13)" data-count="13" id="rule_13" class="formalism"><div class="ruleTitle"><a href="#rule_13" class="internalDFN">Formalism 13 (rule_13)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-190-Frame" class="MathJax"><nobr><span id="MathJax-Span-4182" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4183" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4184" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4185" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4186" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4187" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4188" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4189" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4190" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4191" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4192" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4193" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4195" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4196" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4197" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4198" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4199" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4200" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4202" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4203" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4204" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4205" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4209" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4210" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4211" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-190" type="math/tex">W,\rho \models activity(id,st,et,attrs)</script>
- holds if and only if:</p>
-<ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-191-Frame" class="MathJax"><nobr><span id="MathJax-Span-4212" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4213" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4214" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4215" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-191" type="math/tex">id</script> maps to an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-192-Frame" class="MathJax"><nobr><span id="MathJax-Span-4216" class="math"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4217" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4218" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4219" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4220" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4221" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4222" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4223" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4224" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4225" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4226" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4227" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4228" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4229" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4230" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4232" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4233" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4237" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-192" type="math/tex">act = \rho(id) \in Activities</script>
-</li>
-<li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-193-Frame" class="MathJax"><nobr><span id="MathJax-Span-4238" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4239" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4240" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4241" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-193" type="math/tex">st</script> is specified then it is equal to the start time of the activity, that is: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-194-Frame" class="MathJax"><nobr><span id="MathJax-Span-4242" class="math"><span style="display: inline-block; position: relative; width: 150px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4243" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4244" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4246" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4247" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4248" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4250" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4251" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4252" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4253" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4254" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4255" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4256" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4257" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4258" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4259" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4260" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4261" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4262" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-194" type="math/tex">min(lifetime(id)) = st</script>
-</li>
-<li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-195-Frame" class="MathJax"><nobr><span id="MathJax-Span-4264" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4265" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4266" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4267" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-195" type="math/tex">et</script> is specified then it is equal to the end time of the activity, that is: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-196-Frame" class="MathJax"><nobr><span id="MathJax-Span-4268" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4269" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4270" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4272" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4273" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4274" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4275" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4276" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4277" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4279" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4280" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4281" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4282" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4283" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4284" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4285" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4286" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4287" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4288" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4289" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-196" type="math/tex">max(lifetime(id)) = et</script>
-</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-197-Frame" class="MathJax"><nobr><span id="MathJax-Span-4290" class="math"><span style="display: inline-block; position: relative; width: 137px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4291" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4292" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4293" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4294" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4295" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4296" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4297" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4298" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4300" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4301" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4302" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4303" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4304" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4306" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4307" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4308" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4309" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-197" type="math/tex">match(W,act,attrs)</script>.
-</li>
-</ol>
-</div>
-</section>
-<section id="agent">
-
-<h4><span class="secno">4.3.3 </span> Agent </h4>
-
-<p>An agent formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-198-Frame" class="MathJax"><nobr><span id="MathJax-Span-4310" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4311" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4315" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4317" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4318" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4319" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4320" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4321" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4324" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4325" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4326" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-198" type="math/tex">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-199-Frame" class="MathJax"><nobr><span id="MathJax-Span-4327" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4328" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4329" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4330" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-199" type="math/tex">id</script> denotes the agent and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-200-Frame" class="MathJax"><nobr><span id="MathJax-Span-4331" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4332" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4335" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4336" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4337" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-200" type="math/tex">attrs</script> describes additional attributes.
-</p>
-<div data-title="Formalism 14 (rule_14)" data-count="14" id="rule_14" class="formalism"><div class="ruleTitle"><a href="#rule_14" class="internalDFN">Formalism 14 (rule_14)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-201-Frame" class="MathJax"><nobr><span id="MathJax-Span-4338" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4339" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4340" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4341" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4342" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4343" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4344" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4345" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4346" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4347" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4348" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4349" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4350" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4351" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4353" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4354" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4355" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4356" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4357" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4358" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-201" type="math/tex">W,\rho \models agent(id,attrs)</script> holds if and only if:
- </p>
- <ol>
- <li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-202-Frame" class="MathJax"><nobr><span id="MathJax-Span-4359" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4360" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4361" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4362" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-202" type="math/tex">id</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-203-Frame" class="MathJax"><nobr><span id="MathJax-Span-4363" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4364" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4365" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4366" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4367" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4368" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4369" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4370" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4371" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4372" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4373" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4374" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4375" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4376" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4377" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4379" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-203" type="math/tex">ag = \rho(id) \in Agents</script>
- </li>
- <li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-204-Frame" class="MathJax"><nobr><span id="MathJax-Span-4380" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4381" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4382" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4384" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4385" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4386" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4387" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4388" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4389" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4391" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4392" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4394" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4395" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4396" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4397" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4398" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-204" type="math/tex">match(W,ag,attrs)</script>.
- </li>
- </ol>
-</div>
-</section>
-</section>
-
-<section id="semantics-of-relations">
-<h3><span class="secno">4.4 </span> Semantics of Relations </h3>
-
-
-<section id="generation">
-<h4><span class="secno">4.4.1 </span> Generation </h4>
-
-<p>The generation formula is of the form
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-205-Frame" class="MathJax"><nobr><span id="MathJax-Span-4399" class="math"><span style="display: inline-block; position: relative; width: 227px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4400" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4401" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4402" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4403" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4404" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4405" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4406" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4408" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4409" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4411" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4412" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4413" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4414" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4415" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4416" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4417" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4418" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4419" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4420" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4421" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4422" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4424" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4425" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4428" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4429" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4430" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-205" type="math/tex">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-206-Frame" class="MathJax"><nobr><span id="MathJax-Span-4431" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4432" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4433" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4434" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-206" type="math/tex">id</script> is an event identifier,
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-207-Frame" class="MathJax"><nobr><span id="MathJax-Span-4435" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4436" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4437" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-207" type="math/tex">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-208-Frame" class="MathJax"><nobr><span id="MathJax-Span-4438" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4439" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4440" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-208" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-209-Frame" class="MathJax"><nobr><span id="MathJax-Span-4441" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4442" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4443" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4444" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4445" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4446" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4447" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-209" type="math/tex">attrs</script> is
-a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-210-Frame" class="MathJax"><nobr><span id="MathJax-Span-4448" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4449" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-210" type="math/tex">t</script> is a time.
-</p>
-<div data-title="Formalism 15 (rule_15)" data-count="15" id="rule_15" class="formalism"><div class="ruleTitle"><a href="#rule_15" class="internalDFN">Formalism 15 (rule_15)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-211-Frame" class="MathJax"><nobr><span id="MathJax-Span-4451" class="math"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4452" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4453" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4454" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4455" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4456" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4457" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4459" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4460" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4461" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4462" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4463" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4464" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4466" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4468" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4469" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4470" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4471" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4472" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4473" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4474" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4475" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4476" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4477" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4478" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4481" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4484" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4485" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4486" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-211" type="math/tex">W,\rho \models
- wasGeneratedBy(id,e,a,t,attrs)</script> holds if and only if:
-</p><ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-212-Frame" class="MathJax"><nobr><span id="MathJax-Span-4487" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4488" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4489" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4490" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-212" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-213-Frame" class="MathJax"><nobr><span id="MathJax-Span-4491" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4492" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4493" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4494" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4495" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4496" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4497" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4498" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4499" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4500" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4501" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4502" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4503" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4504" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4505" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4506" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4507" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4508" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-213" type="math/tex">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-214-Frame" class="MathJax"><nobr><span id="MathJax-Span-4509" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4510" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4511" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-214" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-215-Frame" class="MathJax"><nobr><span id="MathJax-Span-4512" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4513" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4514" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4515" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4517" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4518" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4519" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4520" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4521" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4522" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4523" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4524" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4527" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4528" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4529" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4530" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-215" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-216-Frame" class="MathJax"><nobr><span id="MathJax-Span-4531" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4532" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4533" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-216" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-217-Frame" class="MathJax"><nobr><span id="MathJax-Span-4534" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4535" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4536" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4537" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4538" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4539" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4540" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4541" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4542" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4543" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4544" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4545" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4546" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4548" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4549" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4550" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4551" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4552" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4554" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-217" type="math/tex">act = \rho(a) \in Activities</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-218-Frame" class="MathJax"><nobr><span id="MathJax-Span-4555" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4556" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4557" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4558" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4559" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-218" type="math/tex">evt</script> is involved in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-219-Frame" class="MathJax"><nobr><span id="MathJax-Span-4560" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4561" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4562" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4563" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-219" type="math/tex">act</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-220-Frame" class="MathJax"><nobr><span id="MathJax-Span-4565" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4566" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4567" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4569" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4570" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4571" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4572" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4573" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4575" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4576" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4577" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4578" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4579" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4580" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4582" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4583" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4584" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4585" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4586" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4587" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4589" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4591" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-220" type="math/tex">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-221-Frame" class="MathJax"><nobr><span id="MathJax-Span-4592" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4593" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4595" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-221" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-222-Frame" class="MathJax"><nobr><span id="MathJax-Span-4597" class="math"><span style="display: inline-block; position: relative; width: 74px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4598" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4602" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4603" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4604" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4606" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4607" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4608" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-222" type="math/tex">generation</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-223-Frame" class="MathJax"><nobr><span id="MathJax-Span-4609" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4610" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4612" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4613" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4614" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4615" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4616" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4617" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4619" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4620" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4621" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4622" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4623" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4625" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4626" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4628" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4629" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4630" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-223" type="math/tex">type(evt) = generation</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-224-Frame" class="MathJax"><nobr><span id="MathJax-Span-4631" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4632" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4633" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4634" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-224" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-225-Frame" class="MathJax"><nobr><span id="MathJax-Span-4636" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4637" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4638" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-225" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-226-Frame" class="MathJax"><nobr><span id="MathJax-Span-4639" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4640" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4641" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4642" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4643" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4644" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4645" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4646" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4647" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4648" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4649" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4650" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4651" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-226" type="math/tex">time(evt) = t</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-227-Frame" class="MathJax"><nobr><span id="MathJax-Span-4652" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4654" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4655" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4656" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-227" type="math/tex">evt</script> generated <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-228-Frame" class="MathJax"><nobr><span id="MathJax-Span-4657" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4658" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4659" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4660" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-228" type="math/tex">ent</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-229-Frame" class="MathJax"><nobr><span id="MathJax-Span-4662" class="math"><span style="display: inline-block; position: relative; width: 156px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4663" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4664" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4665" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4666" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4668" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4670" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4672" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4673" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4674" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4675" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4676" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4677" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4678" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4680" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4681" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4682" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-229" type="math/tex">(evt,ent) \in Generated</script>.
-</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-230-Frame" class="MathJax"><nobr><span id="MathJax-Span-4683" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4684" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4685" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4686" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4687" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4688" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4689" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4690" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4691" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4693" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4694" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4695" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4700" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4701" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4702" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-230" type="math/tex">match(W,evt,attrs)</script>.
-</li>
-</ol>
-</div>
-
-</section>
-<section id="use">
-<h4><span class="secno">4.4.2 </span> Use </h4>
-
-<p>The use formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-231-Frame" class="MathJax"><nobr><span id="MathJax-Span-4703" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4704" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4705" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4706" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4707" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4708" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4709" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4710" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4711" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4712" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4713" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4714" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4715" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4716" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4718" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4719" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4720" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4721" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4722" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4723" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4724" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-231" type="math/tex">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-232-Frame" class="MathJax"><nobr><span id="MathJax-Span-4725" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4726" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4728" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-232" type="math/tex">id</script> denotes an event, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-233-Frame" class="MathJax"><nobr><span id="MathJax-Span-4729" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4730" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4731" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-233" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-234-Frame" class="MathJax"><nobr><span id="MathJax-Span-4732" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4733" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4734" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-234" type="math/tex">e</script> is an object identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-235-Frame" class="MathJax"><nobr><span id="MathJax-Span-4735" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4737" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4739" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4740" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4741" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-235" type="math/tex">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-236-Frame" class="MathJax"><nobr><span id="MathJax-Span-4742" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4743" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-236" type="math/tex">t</script> is an optional time.
-</p>
-<div data-title="Formalism 16 (rule_16)" data-count="16" id="rule_16" class="formalism"><div class="ruleTitle"><a href="#rule_16" class="internalDFN">Formalism 16 (rule_16)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-237-Frame" class="MathJax"><nobr><span id="MathJax-Span-4745" class="math"><span style="display: inline-block; position: relative; width: 195px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4746" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4747" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4748" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4749" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4750" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4751" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4752" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4753" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4754" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4755" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4756" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4757" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4758" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4759" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4760" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4761" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4762" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4763" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4764" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4765" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4767" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4768" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4769" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4770" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-237" type="math/tex">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
-
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-238-Frame" class="MathJax"><nobr><span id="MathJax-Span-4771" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4772" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4773" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4774" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-238" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-239-Frame" class="MathJax"><nobr><span id="MathJax-Span-4775" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4776" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4778" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4780" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4781" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4782" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4783" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4784" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4785" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4786" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4787" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4788" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4789" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4790" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4792" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-239" type="math/tex">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-240-Frame" class="MathJax"><nobr><span id="MathJax-Span-4793" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4794" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4795" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-240" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-241-Frame" class="MathJax"><nobr><span id="MathJax-Span-4796" class="math"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4797" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4798" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4799" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4801" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4802" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4803" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4804" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4805" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4806" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4807" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4808" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4809" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4812" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4813" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4814" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4815" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4816" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4817" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-241" type="math/tex">act = \rho(id) \in Activities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-242-Frame" class="MathJax"><nobr><span id="MathJax-Span-4818" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4819" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4820" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-242" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-243-Frame" class="MathJax"><nobr><span id="MathJax-Span-4821" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4822" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4823" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4826" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4827" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4829" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4830" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4831" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4832" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4833" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4834" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4835" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4837" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4838" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4839" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-243" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-244-Frame" class="MathJax"><nobr><span id="MathJax-Span-4840" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4841" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4842" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4843" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-244" type="math/tex">evt</script> is part of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-245-Frame" class="MathJax"><nobr><span id="MathJax-Span-4845" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4846" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4847" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4848" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4849" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-245" type="math/tex">act</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-246-Frame" class="MathJax"><nobr><span id="MathJax-Span-4850" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4851" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4852" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4854" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4856" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4857" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4858" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4859" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4860" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4861" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4862" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4863" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4865" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4866" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4867" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4868" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4869" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4870" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4871" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4872" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4873" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4875" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4876" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-246" type="math/tex">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-247-Frame" class="MathJax"><nobr><span id="MathJax-Span-4877" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4878" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4879" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4880" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4881" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-247" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-248-Frame" class="MathJax"><nobr><span id="MathJax-Span-4882" class="math"><span style="display: inline-block; position: relative; width: 23px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4883" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4884" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4885" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4886" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-248" type="math/tex">use</script>, i.e., <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-249-Frame" class="MathJax"><nobr><span id="MathJax-Span-4887" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4888" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4890" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4891" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4892" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4893" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4895" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4896" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4897" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4898" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4899" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4900" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4901" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-249" type="math/tex">type(evt) = use</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-250-Frame" class="MathJax"><nobr><span id="MathJax-Span-4902" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4904" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4905" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4906" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-250" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-251-Frame" class="MathJax"><nobr><span id="MathJax-Span-4907" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4908" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4909" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-251" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-252-Frame" class="MathJax"><nobr><span id="MathJax-Span-4910" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4911" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4912" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4913" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4914" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4915" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4916" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4917" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4918" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4919" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4920" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4921" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4922" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-252" type="math/tex">time(evt) = t</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-253-Frame" class="MathJax"><nobr><span id="MathJax-Span-4923" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4924" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4925" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4926" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4927" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-253" type="math/tex">evt</script> used <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-254-Frame" class="MathJax"><nobr><span id="MathJax-Span-4928" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4929" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4930" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4931" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4932" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-254" type="math/tex">obj</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-255-Frame" class="MathJax"><nobr><span id="MathJax-Span-4933" class="math"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4934" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4936" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4937" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4939" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4940" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4941" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4942" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4943" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4944" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4945" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4946" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4947" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4948" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-255" type="math/tex">(evt,ent) \in Used</script>.
-</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-256-Frame" class="MathJax"><nobr><span id="MathJax-Span-4949" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4950" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4951" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4952" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4954" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4955" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4956" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4957" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4958" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4959" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4960" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4961" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4962" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4963" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4965" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4966" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4967" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4968" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-256" type="math/tex">match(W,evt,attrs)</script>.
-</li></div>
-
-</section>
-<section id="invalidation">
-<h4><span class="secno">4.4.3 </span> Invalidation </h4>
-
-<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-257-Frame" class="MathJax"><nobr><span id="MathJax-Span-4969" class="math"><span style="display: inline-block; position: relative; width: 233px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4970" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4971" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4972" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4973" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4974" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4975" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4976" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4977" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4978" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4979" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4980" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4981" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4982" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4983" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4984" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4985" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4986" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4987" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4988" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4989" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4991" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4992" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4993" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4994" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4996" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4997" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5000" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5001" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5002" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-257" type="math/tex">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-258-Frame" class="MathJax"><nobr><span id="MathJax-Span-5003" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5004" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5005" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5006" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-258" type="math/tex">id</script> is an event identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-259-Frame" class="MathJax"><nobr><span id="MathJax-Span-5007" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5008" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5009" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-259" type="math/tex">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-260-Frame" class="MathJax"><nobr><span id="MathJax-Span-5010" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5011" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5012" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-260" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-261-Frame" class="MathJax"><nobr><span id="MathJax-Span-5013" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5014" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5015" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5017" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5018" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5019" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-261" type="math/tex">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-262-Frame" class="MathJax"><nobr><span id="MathJax-Span-5020" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5021" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5022" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-262" type="math/tex">t</script> is an optional time.</p>
-
-<div data-title="Formalism 17 (rule_17)" data-count="17" id="rule_17" class="formalism"><div class="ruleTitle"><a href="#rule_17" class="internalDFN">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-263-Frame" class="MathJax"><nobr><span id="MathJax-Span-5023" class="math"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5024" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5025" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5027" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5028" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5029" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5032" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5033" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5034" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5035" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5036" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5037" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5038" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5039" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5041" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5042" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5043" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5044" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5045" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5046" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5047" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5048" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5049" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5050" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5051" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5052" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5053" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5054" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5055" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5056" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5057" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5058" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5059" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5060" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-263" type="math/tex">W,\rho \models
- wasInvalidatedBy(id,e,a,t,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-264-Frame" class="MathJax"><nobr><span id="MathJax-Span-5061" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5062" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5064" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-264" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-265-Frame" class="MathJax"><nobr><span id="MathJax-Span-5065" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5066" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5067" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5068" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5069" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5070" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5071" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5072" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5073" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5074" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5075" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5076" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5077" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5078" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5079" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5080" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5081" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5082" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-265" type="math/tex">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-266-Frame" class="MathJax"><nobr><span id="MathJax-Span-5083" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5084" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5085" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-266" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-267-Frame" class="MathJax"><nobr><span id="MathJax-Span-5086" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5087" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5088" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5089" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5091" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5092" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5093" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5094" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5095" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5096" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5097" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5098" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5099" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5100" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5101" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5102" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5103" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5104" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-267" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-268-Frame" class="MathJax"><nobr><span id="MathJax-Span-5105" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5106" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5107" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-268" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-269-Frame" class="MathJax"><nobr><span id="MathJax-Span-5108" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5109" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5110" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5111" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5112" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5113" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5114" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5115" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5116" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5117" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5118" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5119" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5120" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5121" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5122" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5123" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5124" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5125" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5126" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5127" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5128" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-269" type="math/tex">act = \rho(a) \in Activities</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-270-Frame" class="MathJax"><nobr><span id="MathJax-Span-5129" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5130" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5131" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5132" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-270" type="math/tex">evt</script> is involved in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-271-Frame" class="MathJax"><nobr><span id="MathJax-Span-5134" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5135" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5136" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5137" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5138" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-271" type="math/tex">act</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-272-Frame" class="MathJax"><nobr><span id="MathJax-Span-5139" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5140" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5141" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5142" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5143" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5144" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5145" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5146" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5147" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5149" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5150" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5151" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5152" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5154" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5155" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5156" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5157" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5159" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5160" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5161" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5162" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5164" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5165" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-272" type="math/tex">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-273-Frame" class="MathJax"><nobr><span id="MathJax-Span-5166" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5168" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5169" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-273" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-274-Frame" class="MathJax"><nobr><span id="MathJax-Span-5171" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5172" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5173" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5174" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5175" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5176" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5177" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5178" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5179" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5180" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5181" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5182" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5183" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5184" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-274" type="math/tex">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-275-Frame" class="MathJax"><nobr><span id="MathJax-Span-5185" class="math"><span style="display: inline-block; position: relative; width: 166px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5186" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5187" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5188" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5189" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5190" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5191" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5193" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5195" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5196" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5197" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5198" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5199" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5200" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5201" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5202" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5203" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5204" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5205" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5206" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5207" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5208" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-275" type="math/tex">type(evt) = invalidation</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-276-Frame" class="MathJax"><nobr><span id="MathJax-Span-5209" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5210" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5211" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5212" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-276" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-277-Frame" class="MathJax"><nobr><span id="MathJax-Span-5214" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5215" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-277" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-278-Frame" class="MathJax"><nobr><span id="MathJax-Span-5217" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5218" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5219" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5220" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5221" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5222" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5223" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5224" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5225" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5226" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5227" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5228" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-278" type="math/tex">time(evt) = t</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-279-Frame" class="MathJax"><nobr><span id="MathJax-Span-5230" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5231" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5232" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5233" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-279" type="math/tex">evt</script> invalidated <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-280-Frame" class="MathJax"><nobr><span id="MathJax-Span-5235" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5236" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5237" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5238" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5239" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-280" type="math/tex">ent</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-281-Frame" class="MathJax"><nobr><span id="MathJax-Span-5240" class="math"><span style="display: inline-block; position: relative; width: 163px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5241" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5242" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5243" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5244" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5248" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5250" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5251" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5252" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5253" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5254" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5255" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5256" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5257" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5258" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5259" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5260" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5261" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5262" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-281" type="math/tex">(evt,ent) \in Invalidated</script>.
-</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-282-Frame" class="MathJax"><nobr><span id="MathJax-Span-5263" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5264" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5265" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5267" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5268" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5269" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5270" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5271" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5272" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5273" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5274" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5275" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5276" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5277" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5280" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5281" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5282" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-282" type="math/tex">match(W,evt,attrs)</script>.
-</li></ol></div>
-</section>
-
-<section id="association">
-
-<h4><span class="secno">4.4.4 </span> Association </h4>
-
-<p>An association formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-283-Frame" class="MathJax"><nobr><span id="MathJax-Span-5283" class="math"><span style="display: inline-block; position: relative; width: 262px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5284" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5285" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5287" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5288" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5290" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5291" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5292" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5296" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5297" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5298" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5299" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5300" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5301" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5302" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5303" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5304" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5305" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5306" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5307" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5309" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5310" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5311" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5312" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5313" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5317" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5318" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5319" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-283" type="math/tex">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
-
-<div data-title="Formalism 18 (rule_18)" data-count="18" id="rule_18" class="formalism"><div class="ruleTitle"><a href="#rule_18" class="internalDFN">Formalism 18 (rule_18)</a></div><p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-284-Frame" class="MathJax"><nobr><span id="MathJax-Span-5320" class="math"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5321" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5322" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5324" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5325" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5326" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5327" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5328" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5329" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5331" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5332" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5333" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5334" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5338" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5339" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5340" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5341" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5342" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5343" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5344" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5345" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5346" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5347" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5348" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5349" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5350" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5351" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5352" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5354" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5355" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5356" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5357" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5358" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5359" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5360" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-284" type="math/tex">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-285-Frame" class="MathJax"><nobr><span id="MathJax-Span-5361" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5362" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5364" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5365" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5366" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5367" class="mi">c</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-285" type="math/tex">assoc</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-286-Frame" class="MathJax"><nobr><span id="MathJax-Span-5368" class="math"><span style="display: inline-block; position: relative; width: 203px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5369" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5370" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5371" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5372" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5373" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5374" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5375" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5376" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5377" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5378" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5379" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5380" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5381" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5382" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5383" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5384" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5385" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5386" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5387" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5388" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5389" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5390" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5391" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5392" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5393" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-286" type="math/tex">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-287-Frame" class="MathJax"><nobr><span id="MathJax-Span-5394" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5395" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5396" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-287" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-288-Frame" class="MathJax"><nobr><span id="MathJax-Span-5397" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5398" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5399" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5400" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5401" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5402" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5403" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5404" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5405" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5406" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5407" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5408" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5409" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5411" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5412" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5413" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5415" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5416" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5417" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-288" type="math/tex">act = \rho(a) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-289-Frame" class="MathJax"><nobr><span id="MathJax-Span-5418" class="math"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5419" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5420" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5421" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-289" type="math/tex">ag</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-290-Frame" class="MathJax"><nobr><span id="MathJax-Span-5422" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5423" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5425" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5426" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5427" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5429" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5430" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5431" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5432" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5433" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5434" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5435" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5436" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5437" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5438" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5439" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5441" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-290" type="math/tex">agent = \rho(ag) \in Agents</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-291-Frame" class="MathJax"><nobr><span id="MathJax-Span-5442" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5443" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5444" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5445" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-291" type="math/tex">pl</script> is either the placeholder <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-292-Frame" class="MathJax"><nobr><span id="MathJax-Span-5446" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5447" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5448" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-292" type="math/tex">-</script> or denotes a plan <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-293-Frame" class="MathJax"><nobr><span id="MathJax-Span-5449" class="math"><span style="display: inline-block; position: relative; width: 148px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5450" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5451" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5452" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5453" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5454" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5455" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5456" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5457" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5458" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5459" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5460" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5461" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5462" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5463" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5464" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5465" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5466" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-293" type="math/tex">plan=\rho(pl) \in Plans</script>.
-</li>
-<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-294-Frame" class="MathJax"><nobr><span id="MathJax-Span-5467" class="math"><span style="display: inline-block; position: relative; width: 293px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5468" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5469" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5471" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5472" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5473" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5474" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5475" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5476" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5477" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5478" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5479" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5480" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5483" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5484" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5485" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5486" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5487" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5489" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5490" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5491" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5492" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5493" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5494" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5495" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5496" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5497" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5498" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5499" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5500" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5501" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5502" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5504" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5505" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-294" type="math/tex">(assoc,agent,act,plan) \in AssociatedWith</script>.
-</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-295-Frame" class="MathJax"><nobr><span id="MathJax-Span-5506" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5507" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5508" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5509" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5511" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5512" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5513" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5514" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5515" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5516" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5517" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5518" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5519" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5520" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5521" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5522" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5523" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5525" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5526" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5527" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-295" type="math/tex">match(W,assoc,attrs)</script>.
-</li></ol></div>
-</section>
-<section id="start-formulas">
-<h4><span class="secno">4.4.5 </span> Start Formulas </h4>
-
-<p>A start formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-296-Frame" class="MathJax"><nobr><span id="MathJax-Span-5528" class="math"><span style="display: inline-block; position: relative; width: 223px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5529" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5530" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5531" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5532" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5533" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5535" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5536" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5538" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5539" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5540" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5541" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5542" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5543" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5544" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5545" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5546" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5547" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5548" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5549" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5550" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5551" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5552" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5553" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5554" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5555" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5557" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5559" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5560" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5561" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-296" type="math/tex">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
-
-<div data-title="Formalism 19 (rule_19)" data-count="19" id="rule_19" class="formalism"><div class="ruleTitle"><a href="#rule_19" class="internalDFN">Formalism 19 (rule_19)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-297-Frame" class="MathJax"><nobr><span id="MathJax-Span-5562" class="math"><span style="display: inline-block; position: relative; width: 277px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5563" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5564" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5565" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5566" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5567" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5568" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5569" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5570" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5571" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5573" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5574" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5576" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5577" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5578" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5579" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5580" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5581" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5582" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5583" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5585" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5586" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5587" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5588" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5589" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5590" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5591" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5592" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5593" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5597" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5598" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5599" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-297" type="math/tex">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-298-Frame" class="MathJax"><nobr><span id="MathJax-Span-5600" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5601" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5602" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5603" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-298" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-299-Frame" class="MathJax"><nobr><span id="MathJax-Span-5604" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5605" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5606" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5607" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5608" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5609" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5610" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5611" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5612" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5613" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5614" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5615" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5616" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5617" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5618" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5619" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5620" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5621" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-299" type="math/tex">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-300-Frame" class="MathJax"><nobr><span id="MathJax-Span-5622" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5623" class="mrow"><span id="MathJax-Span-5624" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5625" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5626" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-300" type="math/tex">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-301-Frame" class="MathJax"><nobr><span id="MathJax-Span-5627" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5628" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5630" class="mi">c</span><span id="MathJax-Span-5631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5633" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5634" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5635" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5636" class="mo">(</span><span id="MathJax-Span-5637" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5638" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5639" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5640" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5641" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5642" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5643" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5645" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5646" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5647" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5648" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5649" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5651" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-301" type="math/tex">act_2 = \rho(a_2) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-302-Frame" class="MathJax"><nobr><span id="MathJax-Span-5652" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5654" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-302" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-303-Frame" class="MathJax"><nobr><span id="MathJax-Span-5655" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5656" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5657" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5658" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5660" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5661" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5662" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5663" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5664" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5665" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5666" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5667" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5669" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5670" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5672" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5673" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-303" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-304-Frame" class="MathJax"><nobr><span id="MathJax-Span-5674" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5675" class="mrow"><span id="MathJax-Span-5676" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5677" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5678" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-304" type="math/tex">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-305-Frame" class="MathJax"><nobr><span id="MathJax-Span-5679" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5680" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5681" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5682" class="mi">c</span><span id="MathJax-Span-5683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5686" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5687" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5688" class="mo">(</span><span id="MathJax-Span-5689" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5690" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5691" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5692" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5693" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5694" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5695" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5697" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5698" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5699" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5700" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5701" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5702" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5703" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-305" type="math/tex">act_1 = \rho(a_1) \in Activities</script>.
-</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-306-Frame" class="MathJax"><nobr><span id="MathJax-Span-5704" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5705" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5706" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5707" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-306" type="math/tex">evt</script> has type <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-307-Frame" class="MathJax"><nobr><span id="MathJax-Span-5709" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5710" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5711" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5713" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5715" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-307" type="math/tex">start</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-308-Frame" class="MathJax"><nobr><span id="MathJax-Span-5716" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5717" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5719" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5720" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5721" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5722" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5723" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5724" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5725" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5726" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5727" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5728" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5729" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5730" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5731" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5732" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-308" type="math/tex">type(evt) = start</script>.
-</li>
-<li>The event happened at the start of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-309-Frame" class="MathJax"><nobr><span id="MathJax-Span-5733" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5734" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5735" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5736" class="mi">c</span><span id="MathJax-Span-5737" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5739" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-309" type="math/tex">act_2</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-310-Frame" class="MathJax"><nobr><span id="MathJax-Span-5740" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5741" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5742" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5743" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5744" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5747" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5748" class="mi">c</span><span id="MathJax-Span-5749" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5750" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5751" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5752" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5753" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5754" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5755" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5757" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5758" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5759" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5760" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5761" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5762" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5764" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5765" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5767" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5768" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5769" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-310" type="math/tex">(evt,act_2)
- \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-311-Frame" class="MathJax"><nobr><span id="MathJax-Span-5770" class="math"><span style="display: inline-block; position: relative; width: 214px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5771" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5772" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5773" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5774" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5775" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5776" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5778" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5779" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5780" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5781" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5782" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5783" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5784" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5785" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5786" class="mi">c</span><span id="MathJax-Span-5787" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5789" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5790" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5791" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5792" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5793" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5794" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5795" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5796" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5797" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5799" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5801" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-311" type="math/tex">min(lifetime(act_2)) = time(evt)</script>.
-</li>
-<li>TODO: The entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-312-Frame" class="MathJax"><nobr><span id="MathJax-Span-5802" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5803" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5804" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-312" type="math/tex">e</script> was generated by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-313-Frame" class="MathJax"><nobr><span id="MathJax-Span-5805" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5806" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5807" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5808" class="mi">c</span><span id="MathJax-Span-5809" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5811" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-313" type="math/tex">act_1</script> and started <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-314-Frame" class="MathJax"><nobr><span id="MathJax-Span-5812" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5813" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5814" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5815" class="mi">c</span><span id="MathJax-Span-5816" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5818" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-314" type="math/tex">act_2</script>.
-</li><li>The event happened during <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-315-Frame" class="MathJax"><nobr><span id="MathJax-Span-5819" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5820" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5822" class="mi">c</span><span id="MathJax-Span-5823" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5824" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5825" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-315" type="math/tex">act_1</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-316-Frame" class="MathJax"><nobr><span id="MathJax-Span-5826" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5827" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5829" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5830" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5832" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5833" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5834" class="mi">c</span><span id="MathJax-Span-5835" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5837" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5838" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5839" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5840" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5841" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5842" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5843" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5845" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5846" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5847" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5848" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5849" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5850" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5851" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5853" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5854" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5855" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-316" type="math/tex">(evt,act_1)
- \in EventsActivities</script>.
-</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-317-Frame" class="MathJax"><nobr><span id="MathJax-Span-5856" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5857" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5858" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5861" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5862" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5863" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5864" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5865" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5866" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5867" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5869" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5870" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5871" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5872" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5873" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5874" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5875" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-317" type="math/tex">match(W,evt,attrs)</script>.
-</li></ol></div>
-</section>
-<section id="end">
-<h4><span class="secno">4.4.6 </span> End </h4>
-
-<p>An activity end formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-318-Frame" class="MathJax"><nobr><span id="MathJax-Span-5876" class="math"><span style="display: inline-block; position: relative; width: 217px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5877" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5878" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5879" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5880" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5881" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5882" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5883" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5884" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5885" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5886" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5887" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5888" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5889" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5890" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5891" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5892" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5893" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5894" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5895" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5896" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5897" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5898" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5899" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5900" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5901" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5902" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5905" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5906" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5907" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-318" type="math/tex">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
-
-<div data-title="Formalism 20 (rule_20)" data-count="20" id="rule_20" class="formalism"><div class="ruleTitle"><a href="#rule_20" class="internalDFN">Formalism 20 (rule_20)</a></div>
-<p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-319-Frame" class="MathJax"><nobr><span id="MathJax-Span-5908" class="math"><span style="display: inline-block; position: relative; width: 271px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5909" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5910" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5911" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5912" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5913" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5914" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5916" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5917" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5918" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5919" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5920" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5921" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5922" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5923" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5924" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5925" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5926" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5927" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5928" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5929" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5930" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5931" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5932" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5933" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5934" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5935" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5936" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5937" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5938" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5939" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5941" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5942" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5943" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-319" type="math/tex">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</script> holds if and only
- if:</p>
-
-<ol>
- <li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-320-Frame" class="MathJax"><nobr><span id="MathJax-Span-5944" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5945" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5946" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5947" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-320" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-321-Frame" class="MathJax"><nobr><span id="MathJax-Span-5948" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5949" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5951" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5953" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5954" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5955" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5956" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5957" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5958" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5959" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5960" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5961" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5962" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5963" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5965" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-321" type="math/tex">evt = \rho(id) \in Events</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-322-Frame" class="MathJax"><nobr><span id="MathJax-Span-5966" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5967" class="mrow"><span id="MathJax-Span-5968" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5969" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5970" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-322" type="math/tex">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-323-Frame" class="MathJax"><nobr><span id="MathJax-Span-5971" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5972" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5973" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5974" class="mi">c</span><span id="MathJax-Span-5975" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5976" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5977" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5978" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5979" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5980" class="mo">(</span><span id="MathJax-Span-5981" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5982" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5983" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5984" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5985" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5986" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5987" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5989" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5990" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5991" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5994" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5995" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-323" type="math/tex">act_2 = \rho(a_2)\in Activities</script>.</li>
-<li> [WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-324-Frame" class="MathJax"><nobr><span id="MathJax-Span-5996" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5997" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5998" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-324" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-325-Frame" class="MathJax"><nobr><span id="MathJax-Span-5999" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6000" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6001" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6002" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6003" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6004" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6005" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6006" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6007" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6008" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6009" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6010" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6011" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6012" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6013" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6016" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6017" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-325" type="math/tex">ent = \rho(e)\in Entities</script>.</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-326-Frame" class="MathJax"><nobr><span id="MathJax-Span-6018" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-6019" class="mrow"><span id="MathJax-Span-6020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6021" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6022" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-326" type="math/tex">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-327-Frame" class="MathJax"><nobr><span id="MathJax-Span-6023" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6024" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6025" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6026" class="mi">c</span><span id="MathJax-Span-6027" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6029" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6030" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6031" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6032" class="mo">(</span><span id="MathJax-Span-6033" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6034" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6035" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6036" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6037" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6038" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6039" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6042" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6045" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6046" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6047" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-327" type="math/tex">act_1 = \rho(a_1)\in Activities</script>.</li>
-<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-328-Frame" class="MathJax"><nobr><span id="MathJax-Span-6048" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6049" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6050" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6051" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-328" type="math/tex">evt</script> has type <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-329-Frame" class="MathJax"><nobr><span id="MathJax-Span-6053" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6054" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6055" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6056" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6057" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-329" type="math/tex">end</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-330-Frame" class="MathJax"><nobr><span id="MathJax-Span-6058" class="math"><span style="display: inline-block; position: relative; width: 108px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6059" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6061" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6062" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6063" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6064" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6066" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6068" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6069" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6070" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6071" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6072" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-330" type="math/tex">type(evt) = end</script>.</li>
-<li>The event happened at the end of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-331-Frame" class="MathJax"><nobr><span id="MathJax-Span-6073" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6074" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6075" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6076" class="mi">c</span><span id="MathJax-Span-6077" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6078" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6079" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-331" type="math/tex">act_2</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-332-Frame" class="MathJax"><nobr><span id="MathJax-Span-6080" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6081" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6082" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6083" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6084" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6085" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6086" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6087" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6088" class="mi">c</span><span id="MathJax-Span-6089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6091" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6092" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6093" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6094" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6095" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6096" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6097" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6098" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6099" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6100" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6101" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6102" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6103" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6104" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6105" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6106" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6107" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6108" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6109" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-332" type="math/tex">(evt,act_2)
- \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-333-Frame" class="MathJax"><nobr><span id="MathJax-Span-6110" class="math"><span style="display: inline-block; position: relative; width: 217px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6111" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6112" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6113" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6114" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6115" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6116" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6117" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6118" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6119" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6122" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6123" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6124" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6125" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6126" class="mi">c</span><span id="MathJax-Span-6127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6129" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6130" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6131" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6132" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6134" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6135" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6136" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6137" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6138" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6139" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6141" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-333" type="math/tex">max(lifetime(act_2)) = time(evt)</script>.</li>
- <li>TODO: The entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-334-Frame" class="MathJax"><nobr><span id="MathJax-Span-6142" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6143" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6144" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-334" type="math/tex">e</script> was generated by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-335-Frame" class="MathJax"><nobr><span id="MathJax-Span-6145" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6146" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6147" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6148" class="mi">c</span><span id="MathJax-Span-6149" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6150" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6151" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-335" type="math/tex">act_1</script> and ended <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-336-Frame" class="MathJax"><nobr><span id="MathJax-Span-6152" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6153" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6154" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6155" class="mi">c</span><span id="MathJax-Span-6156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6157" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6158" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-336" type="math/tex">act_2</script>.</li>
-
-<li>The event happened during <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-337-Frame" class="MathJax"><nobr><span id="MathJax-Span-6159" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6160" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6161" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6162" class="mi">c</span><span id="MathJax-Span-6163" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6164" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6165" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-337" type="math/tex">act_1</script>, that is, $(evt,act_1) \in EventActivities.</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-338-Frame" class="MathJax"><nobr><span id="MathJax-Span-6166" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6168" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6169" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6171" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6172" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6173" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6174" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6175" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6176" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6177" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6178" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6179" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6180" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6181" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6182" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6183" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6184" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6185" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-338" type="math/tex">match(W,evt,attrs)</script>.</li>
-</ol>
-</div>
-</section>
-
-<section id="attribution">
-<h4><span class="secno">4.4.7 </span> Attribution </h4>
-
-<p>
-An attribution formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-339-Frame" class="MathJax"><nobr><span id="MathJax-Span-6186" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6187" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6188" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6189" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6190" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6191" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6192" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6194" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6195" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6196" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6197" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6199" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6200" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6201" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6202" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6203" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6204" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6205" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6206" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6207" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6208" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6209" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6210" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6211" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6212" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6215" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6216" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6217" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-339" type="math/tex">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
-</p>
-<div data-title="Formalism 21 (rule_21)" data-count="21" id="rule_21" class="formalism"><div class="ruleTitle"><a href="#rule_21" class="internalDFN">Formalism 21 (rule_21)</a></div>
- <p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-340-Frame" class="MathJax"><nobr><span id="MathJax-Span-6218" class="math"><span style="display: inline-block; position: relative; width: 276px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6219" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6220" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6221" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6222" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6223" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6224" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6226" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6227" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6230" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6232" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6233" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6235" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6236" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6237" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6238" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6239" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6240" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6241" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6242" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6243" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6244" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6245" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6246" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6247" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6248" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6251" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6252" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6253" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-340" type="math/tex">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
- holds if and only if:
- </p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-341-Frame" class="MathJax"><nobr><span id="MathJax-Span-6254" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6255" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6256" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6257" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-341" type="math/tex">id</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-342-Frame" class="MathJax"><nobr><span id="MathJax-Span-6258" class="math"><span style="display: inline-block; position: relative; width: 203px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6259" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6261" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6262" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6263" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6264" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6265" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6266" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6267" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6268" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6269" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6270" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6271" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6272" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6273" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6274" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6275" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6276" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6277" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6280" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6281" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6282" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6283" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-342" type="math/tex">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-343-Frame" class="MathJax"><nobr><span id="MathJax-Span-6284" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6285" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6286" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-343" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-344-Frame" class="MathJax"><nobr><span id="MathJax-Span-6287" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6288" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6289" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6290" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6292" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6293" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6294" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6295" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6296" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6297" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6298" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6299" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6300" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6301" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6302" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6303" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6304" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6305" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-344" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-345-Frame" class="MathJax"><nobr><span id="MathJax-Span-6306" class="math"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6307" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6309" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-345" type="math/tex">ag</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-346-Frame" class="MathJax"><nobr><span id="MathJax-Span-6310" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6311" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6315" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6317" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6318" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6319" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6321" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6322" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6323" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6324" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6325" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6326" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6327" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6328" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6329" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-346" type="math/tex">agent = \rho(ag) \in Agents</script>.
-</li>
-<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-347-Frame" class="MathJax"><nobr><span id="MathJax-Span-6330" class="math"><span style="display: inline-block; position: relative; width: 236px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6331" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6332" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6334" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6335" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6336" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6337" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6338" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6339" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6340" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6341" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6342" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6343" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6344" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6345" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6346" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6348" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6349" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6350" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6351" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6352" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6353" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6354" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6355" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6356" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6357" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6358" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6359" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6360" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6361" class="mi">o</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-347" type="math/tex">(assoc,ent,agent) \in AttributedTo</script>.
-</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-348-Frame" class="MathJax"><nobr><span id="MathJax-Span-6362" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6363" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6364" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6365" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6367" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6368" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6369" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6370" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6371" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6372" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6373" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6376" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6377" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6379" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6380" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6381" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-348" type="math/tex">match(W,evt,attrs)</script>.
-</li></ol>
-</div>
-</section>
-
-<section id="communication">
-<h4><span class="secno">4.4.8 </span>Communication</h4>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Communication</div></div>
-
-</section>
-
-
-<section id="responsibility">
-
-<h4><span class="secno">4.4.9 </span> Responsibility </h4>
-
-<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-349-Frame" class="MathJax"><nobr><span id="MathJax-Span-6382" class="math"><span style="display: inline-block; position: relative; width: 284px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6383" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6384" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6385" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6386" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6387" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6388" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6389" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6390" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6391" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6392" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6393" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6394" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6395" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6396" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6397" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6398" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6399" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6400" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6401" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6402" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6403" class="mi">a</span><span id="MathJax-Span-6404" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6405" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6406" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6407" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6408" class="mi">a</span><span id="MathJax-Span-6409" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6410" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6411" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6412" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6413" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6414" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6416" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6417" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6418" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6419" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6420" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6421" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6422" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-349" type="math/tex">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-350-Frame" class="MathJax"><nobr><span id="MathJax-Span-6423" class="math"><span style="display: inline-block; position: relative; width: 56px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6424" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6425" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6426" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6428" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6429" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6430" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6431" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-350" type="math/tex">ActsFor</script> relation as follows:</p>
-
-<div data-title="Formalism 22 (rule_22)" data-count="22" id="rule_22" class="formalism"><div class="ruleTitle"><a href="#rule_22" class="internalDFN">Formalism 22 (rule_22)</a></div>
- <p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-351-Frame" class="MathJax"><nobr><span id="MathJax-Span-6432" class="math"><span style="display: inline-block; position: relative; width: 338px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6433" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6434" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6435" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6436" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6437" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6439" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6441" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6442" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6443" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6444" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6445" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6446" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6447" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6449" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6450" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6451" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6452" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6453" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6454" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6455" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6456" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6457" class="mi">a</span><span id="MathJax-Span-6458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6459" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6460" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6462" class="mi">a</span><span id="MathJax-Span-6463" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6464" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6465" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6466" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6467" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6468" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6469" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6470" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6471" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6472" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6473" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6474" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6475" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6476" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-351" type="math/tex">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-352-Frame" class="MathJax"><nobr><span id="MathJax-Span-6477" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6478" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6479" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6480" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-352" type="math/tex">id</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-353-Frame" class="MathJax"><nobr><span id="MathJax-Span-6481" class="math"><span style="display: inline-block; position: relative; width: 199px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6482" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6483" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6485" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6486" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6487" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6488" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6489" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6490" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6492" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6493" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6494" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6495" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6496" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6497" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6498" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6499" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6500" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6501" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6502" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6503" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6504" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6505" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-353" type="math/tex">deleg=\rho(id) \in Delegations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-354-Frame" class="MathJax"><nobr><span id="MathJax-Span-6506" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6507" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6508" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-354" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-355-Frame" class="MathJax"><nobr><span id="MathJax-Span-6509" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6510" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6511" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6512" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6513" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6514" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6515" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6516" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6517" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6518" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6519" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6520" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6521" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6522" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6523" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6524" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6525" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6527" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6528" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6529" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-355" type="math/tex">act=\rho(a) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-356-Frame" class="MathJax"><nobr><span id="MathJax-Span-6530" class="math"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6531" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6532" class="mi">a</span><span id="MathJax-Span-6533" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6534" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6535" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6537" class="mi">a</span><span id="MathJax-Span-6538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6539" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6540" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.855em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-356" type="math/tex">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-357-Frame" class="MathJax"><nobr><span id="MathJax-Span-6541" class="math"><span style="display: inline-block; position: relative; width: 299px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6542" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6544" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6545" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6546" class="mi">n</span><span id="MathJax-Span-6547" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6549" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6550" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6551" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6552" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6553" class="mi">a</span><span id="MathJax-Span-6554" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6555" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6556" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6557" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6558" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6560" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6561" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6562" class="mi">n</span><span id="MathJax-Span-6563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6565" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6566" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6567" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6568" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6569" class="mi">a</span><span id="MathJax-Span-6570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6571" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6572" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6573" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6574" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6575" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6576" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6577" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6578" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6579" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6580" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.107em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-357" type="math/tex">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
-</li>
-<li>The agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-358-Frame" class="MathJax"><nobr><span id="MathJax-Span-6581" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6582" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6583" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6584" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6585" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6586" class="mi">n</span><span id="MathJax-Span-6587" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6589" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-358" type="math/tex">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-359-Frame" class="MathJax"><nobr><span id="MathJax-Span-6590" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6591" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6592" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6593" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6595" class="mi">n</span><span id="MathJax-Span-6596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6598" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-359" type="math/tex">agent_1</script> with respect to the activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-360-Frame" class="MathJax"><nobr><span id="MathJax-Span-6599" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6600" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6601" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6602" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-360" type="math/tex">act</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-361-Frame" class="MathJax"><nobr><span id="MathJax-Span-6604" class="math"><span style="display: inline-block; position: relative; width: 261px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6605" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6606" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6607" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6608" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6609" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6610" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6611" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6612" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6613" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6614" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6615" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6616" class="mi">n</span><span id="MathJax-Span-6617" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6619" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6620" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6621" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6622" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6623" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6624" class="mi">n</span><span id="MathJax-Span-6625" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6626" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6627" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6628" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6630" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6632" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6633" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6634" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6635" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6637" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6638" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6639" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6640" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-361" type="math/tex">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
-</li>
-<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-362-Frame" class="MathJax"><nobr><span id="MathJax-Span-6641" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6642" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6643" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6644" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6645" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6647" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6648" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6649" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6650" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6651" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6652" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6653" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6654" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6655" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6657" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6661" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6662" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-362" type="math/tex">match(W,assoc,attrs)</script>.
-</li></ol></div>
-</section>
-
-
-<section id="derivation">
-
-<h4><span class="secno">4.4.10 </span> Derivation </h4>
-
-<section id="precise">
-<h5><span class="secno">4.4.10.1 </span> Precise </h5>
-
-<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-363-Frame" class="MathJax"><nobr><span id="MathJax-Span-6663" class="math"><span style="display: inline-block; position: relative; width: 280px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6664" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6665" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6668" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6670" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6672" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6673" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6674" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6675" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6676" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6677" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6678" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6679" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6680" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6681" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6682" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6684" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6685" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6686" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6687" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6688" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6689" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6690" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6691" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6693" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6694" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6695" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6700" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6701" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6702" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-363" type="math/tex">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
-</p>
-<div data-title="Formalism 23 (rule_23)" data-count="23" id="rule_23" class="formalism"><div class="ruleTitle"><a href="#rule_23" class="internalDFN">Formalism 23 (rule_23)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-364-Frame" class="MathJax"><nobr><span id="MathJax-Span-6703" class="math"><span style="display: inline-block; position: relative; width: 347px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6704" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6705" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6706" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6707" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6708" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6709" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6710" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6711" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6712" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6713" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6715" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6716" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6717" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6718" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6719" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6720" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6721" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6722" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6723" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6724" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6725" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6726" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6727" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6728" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6729" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6733" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6735" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6736" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6737" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6738" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6739" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6740" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6741" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6742" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6743" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6746" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6747" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6748" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-364" type="math/tex">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-365-Frame" class="MathJax"><nobr><span id="MathJax-Span-6749" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6750" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6751" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6752" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-365" type="math/tex">id</script> denotes a derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-366-Frame" class="MathJax"><nobr><span id="MathJax-Span-6753" class="math"><span style="display: inline-block; position: relative; width: 196px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6754" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6755" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6757" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6758" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6759" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6760" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6761" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6762" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6764" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6765" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6766" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6767" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6768" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6769" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6771" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6772" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6773" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6774" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6775" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6776" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6777" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-366" type="math/tex">deriv = \rho(id) \in Derivations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-367-Frame" class="MathJax"><nobr><span id="MathJax-Span-6778" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6779" class="mrow"><span id="MathJax-Span-6780" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6781" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6782" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6783" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6785" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6786" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-367" type="math/tex">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-368-Frame" class="MathJax"><nobr><span id="MathJax-Span-6787" class="math"><span style="display: inline-block; position: relative; width: 255px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6788" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6789" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6790" class="mi">n</span><span id="MathJax-Span-6791" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6792" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6793" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6794" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6795" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6796" class="mo">(</span><span id="MathJax-Span-6797" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6798" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6800" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6801" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6802" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6803" class="mi">n</span><span id="MathJax-Span-6804" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6805" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6806" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6807" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6808" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6809" class="mo">(</span><span id="MathJax-Span-6810" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6811" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6812" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6813" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6814" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6815" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6816" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6818" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6819" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6820" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6822" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-368" type="math/tex">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script> .
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-369-Frame" class="MathJax"><nobr><span id="MathJax-Span-6823" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6824" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6825" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-369" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-370-Frame" class="MathJax"><nobr><span id="MathJax-Span-6826" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6827" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6828" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6829" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6830" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6831" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6832" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6833" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6834" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6835" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6836" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6837" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6838" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6840" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6841" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6844" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6845" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6846" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-370" type="math/tex">act = \rho(a) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-371-Frame" class="MathJax"><nobr><span id="MathJax-Span-6847" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6848" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6849" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-371" type="math/tex">g</script> denotes a generation event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-372-Frame" class="MathJax"><nobr><span id="MathJax-Span-6850" class="math"><span style="display: inline-block; position: relative; width: 143px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6851" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6852" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6854" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6855" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6856" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6857" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6858" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6859" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6860" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6861" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6862" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6863" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6864" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6865" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6866" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-372" type="math/tex">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-373-Frame" class="MathJax"><nobr><span id="MathJax-Span-6867" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6868" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6869" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6870" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6871" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6872" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6873" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6874" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6875" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6876" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6877" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6878" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6879" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6880" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6881" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6882" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6883" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6884" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6885" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6886" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6887" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6888" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6889" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-373" type="math/tex">type(\rho(g)) = generation</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-374-Frame" class="MathJax"><nobr><span id="MathJax-Span-6890" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6891" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6892" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-374" type="math/tex">u</script> denotes a use event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-375-Frame" class="MathJax"><nobr><span id="MathJax-Span-6893" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6894" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6895" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6896" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6897" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6898" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6899" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6900" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6901" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6902" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6903" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6905" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-375" type="math/tex">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-376-Frame" class="MathJax"><nobr><span id="MathJax-Span-6906" class="math"><span style="display: inline-block; position: relative; width: 114px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6907" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6908" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6909" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6910" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6911" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6912" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6913" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6914" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6915" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6916" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6917" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6918" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6919" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6920" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6921" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-376" type="math/tex">type(\rho(u)) = use</script>.
-</li>
-<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-377-Frame" class="MathJax"><nobr><span id="MathJax-Span-6922" class="math"><span style="display: inline-block; position: relative; width: 339px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6923" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6924" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6925" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6926" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6927" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6928" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6929" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6930" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6931" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6933" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6934" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6936" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6939" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6940" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6941" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6942" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6943" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6944" class="mi">n</span><span id="MathJax-Span-6945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6946" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6947" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6948" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6949" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6951" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6952" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6953" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6954" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6955" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6956" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6957" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6958" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6959" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6960" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6961" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6962" class="mi">n</span><span id="MathJax-Span-6963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-377" type="math/tex">derivedFrom(deriv) =
-ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
-</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-378-Frame" class="MathJax"><nobr><span id="MathJax-Span-6966" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6967" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6968" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6971" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6972" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6973" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6974" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6975" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6976" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6977" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6978" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6979" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6980" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6981" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6984" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6986" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6987" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-378" type="math/tex">match(W,deriv,attrs)</script>.</li>
-</ol>
-</div>
-</section>
-<section id="imprecise">
-
-<h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
-<p>
-An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-379-Frame" class="MathJax"><nobr><span id="MathJax-Span-6988" class="math"><span style="display: inline-block; position: relative; width: 289px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6989" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6990" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6991" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6992" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6993" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6994" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6995" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6996" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6997" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6998" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7000" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7001" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7002" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7003" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7004" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7005" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7006" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7007" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7008" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7009" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7010" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7011" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7012" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7013" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7014" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7015" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7016" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7017" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7018" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7019" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7020" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7023" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7025" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7026" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7027" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-379" type="math/tex">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
-
-<div data-title="Formalism 24 (rule_24)" data-count="24" id="rule_24" class="formalism"><div class="ruleTitle"><a href="#rule_24" class="internalDFN">Formalism 24 (rule_24)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-380-Frame" class="MathJax"><nobr><span id="MathJax-Span-7028" class="math"><span style="display: inline-block; position: relative; width: 343px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7029" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7030" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7031" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7032" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7033" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7034" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7035" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7036" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7037" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7038" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7039" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7040" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7041" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7042" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7043" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7044" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7045" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7046" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7047" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7048" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7049" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7050" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7054" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7058" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7059" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7060" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7061" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7062" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7063" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7064" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7065" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7066" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7068" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7069" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7070" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7071" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-380" type="math/tex">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
-<ol>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-381-Frame" class="MathJax"><nobr><span id="MathJax-Span-7072" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7073" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7074" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7075" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-381" type="math/tex">id</script> denotes a derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-382-Frame" class="MathJax"><nobr><span id="MathJax-Span-7076" class="math"><span style="display: inline-block; position: relative; width: 196px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7077" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7078" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7079" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7080" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7082" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7083" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7084" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7085" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7086" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7087" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7088" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7089" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7090" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7091" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7092" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7093" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7094" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7095" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7096" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7097" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7098" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7099" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7100" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-382" type="math/tex">deriv = \rho(id) \in Derivations</script>
-</li>
-<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-383-Frame" class="MathJax"><nobr><span id="MathJax-Span-7101" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7102" class="mrow"><span id="MathJax-Span-7103" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7104" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7105" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7106" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7109" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-383" type="math/tex">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-384-Frame" class="MathJax"><nobr><span id="MathJax-Span-7110" class="math"><span style="display: inline-block; position: relative; width: 255px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7111" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7112" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7113" class="mi">n</span><span id="MathJax-Span-7114" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7116" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7117" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7118" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7119" class="mo">(</span><span id="MathJax-Span-7120" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7121" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7122" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7123" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7124" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7125" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7126" class="mi">n</span><span id="MathJax-Span-7127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7129" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7130" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7131" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7132" class="mo">(</span><span id="MathJax-Span-7133" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7134" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7135" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7136" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7137" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7138" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7139" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7141" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7142" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7143" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7145" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-384" type="math/tex">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script>
-</li>
-<li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-385-Frame" class="MathJax"><nobr><span id="MathJax-Span-7146" class="math"><span style="display: inline-block; position: relative; width: 256px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7147" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7148" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7149" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7150" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7151" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7152" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7154" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7155" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7156" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7157" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7158" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7159" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7160" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7161" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7162" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7164" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7165" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7166" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7167" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7168" class="mi">n</span><span id="MathJax-Span-7169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7171" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-7172" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-7173" class="mi">w</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-7174" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-7175" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7176" class="mi">n</span><span id="MathJax-Span-7177" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7178" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7179" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-385" type="math/tex">derivedFrom(deriv)= ent_2 \cdot w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-386-Frame" class="MathJax"><nobr><span id="MathJax-Span-7180" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7181" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7182" class="mi">w</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.616em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-386" type="math/tex">w</script>
-</li>
-<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-387-Frame" class="MathJax"><nobr><span id="MathJax-Span-7183" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7184" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7185" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7187" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7188" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7189" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7190" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7191" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7192" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7193" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7194" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7195" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7197" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7198" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7199" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7200" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7202" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7203" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7204" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-387" type="math/tex">match(W,deriv,attrs)</script>.
-</li></ol></div>
-</section>
-</section>
-
- <section id="influence">
- <h4><span class="secno">4.4.11 </span>Influence</h4>
-
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Define influence semantics.</div></div>
-
- </section>
-
-<section id="specialization">
-<h4><span class="secno">4.4.12 </span> Specialization </h4>
-
-<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-388-Frame" class="MathJax"><nobr><span id="MathJax-Span-7205" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7206" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7207" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7208" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7209" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7210" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7211" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7212" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7213" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7214" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7215" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7216" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7217" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7218" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7219" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7220" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7221" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7222" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7223" class="mo">(</span><span id="MathJax-Span-7224" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7225" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7226" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7227" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7228" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7229" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7230" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7231" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-388" type="math/tex">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.
-</p>
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">
- <p>TODO: The content of this definition may be moved into the
- structure W via an irreflexive/transitive specialization relation, since by
- itself this definition is not transitive.</p>
- </div></div>
-
-<div data-title="Formalism 25 (rule_25)" data-count="25" id="rule_25" class="formalism"><div class="ruleTitle"><a href="#rule_25" class="internalDFN">Formalism 25 (rule_25)</a></div> <p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-389-Frame" class="MathJax"><nobr><span id="MathJax-Span-7232" class="math"><span style="display: inline-block; position: relative; width: 219px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7233" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7234" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7235" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7236" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7237" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7238" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7239" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7240" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7241" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7242" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7246" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7247" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7250" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7251" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7252" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7253" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7254" class="mo">(</span><span id="MathJax-Span-7255" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7256" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7257" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7258" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7259" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7260" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7261" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7262" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-389" type="math/tex">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
-<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-390-Frame" class="MathJax"><nobr><span id="MathJax-Span-7263" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7264" class="mrow"><span id="MathJax-Span-7265" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7266" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7267" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-390" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-391-Frame" class="MathJax"><nobr><span id="MathJax-Span-7268" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7269" class="mrow"><span id="MathJax-Span-7270" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7271" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7272" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-391" type="math/tex">e_2</script> are entity identifiers, denoting
- distinct entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-392-Frame" class="MathJax"><nobr><span id="MathJax-Span-7273" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7274" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7276" class="mi">n</span><span id="MathJax-Span-7277" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7279" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7280" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7281" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7282" class="mo">(</span><span id="MathJax-Span-7283" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7284" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7285" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7286" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7287" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7288" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7289" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7290" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7291" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7292" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7294" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7295" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-392" type="math/tex">ent_1
- = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-393-Frame" class="MathJax"><nobr><span id="MathJax-Span-7296" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7297" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7298" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7299" class="mi">n</span><span id="MathJax-Span-7300" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7301" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7302" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7303" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7304" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7305" class="mo">(</span><span id="MathJax-Span-7306" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7307" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7308" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7309" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7310" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7311" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7312" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7314" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7316" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7317" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7318" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-393" type="math/tex">ent_2 = \rho(e_2) \in Entities</script>,
- where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-394-Frame" class="MathJax"><nobr><span id="MathJax-Span-7319" class="math"><span style="display: inline-block; position: relative; width: 79px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.901em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7320" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7321" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7322" class="mi">n</span><span id="MathJax-Span-7323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7324" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7326" class="mo">≠</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7327" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7328" class="mi">n</span><span id="MathJax-Span-7329" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7330" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7331" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-394" type="math/tex">ent_1 \neq ent_2</script>.
-</li>
-<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-395-Frame" class="MathJax"><nobr><span id="MathJax-Span-7332" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7333" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7335" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7337" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7338" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7339" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7340" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7341" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7342" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7343" class="mi">n</span><span id="MathJax-Span-7344" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7345" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7346" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7347" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7348" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7350" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7351" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7352" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7353" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7354" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7355" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7356" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7357" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7358" class="mi">n</span><span id="MathJax-Span-7359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7360" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7361" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7362" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-395" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>.
-</li>
-<li>The lifetime of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-396-Frame" class="MathJax"><nobr><span id="MathJax-Span-7363" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7364" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7365" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7366" class="mi">b</span><span id="MathJax-Span-7367" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7368" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7369" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-396" type="math/tex">obj_1</script> is contained in that of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-397-Frame" class="MathJax"><nobr><span id="MathJax-Span-7370" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7371" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7372" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7373" class="mi">n</span><span id="MathJax-Span-7374" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7376" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-397" type="math/tex">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-398-Frame" class="MathJax"><nobr><span id="MathJax-Span-7377" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7378" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7379" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7380" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7381" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7382" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7384" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7385" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7386" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7387" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7389" class="mi">n</span><span id="MathJax-Span-7390" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7392" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7393" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7394" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7395" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7396" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7397" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7398" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7400" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7401" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7402" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7403" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7404" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7405" class="mi">n</span><span id="MathJax-Span-7406" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7407" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7408" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7409" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-398" type="math/tex">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
-</li>
-<li>For each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-399-Frame" class="MathJax"><nobr><span id="MathJax-Span-7410" class="math"><span style="display: inline-block; position: relative; width: 26px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7411" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7412" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7415" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-399" type="math/tex">attr</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-400-Frame" class="MathJax"><nobr><span id="MathJax-Span-7416" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7417" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7418" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7419" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7420" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7421" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7422" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7423" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7424" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7425" class="mi">b</span><span id="MathJax-Span-7426" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7427" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7428" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7429" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7430" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7433" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7434" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7435" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7436" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7437" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7438" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7439" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7440" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7441" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7442" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7443" class="mi">b</span><span id="MathJax-Span-7444" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7445" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7446" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7447" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7451" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7452" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-400" type="math/tex">value(obj_1,attr) \supseteq value(obj_2,attr)</script>.
-</li></ol></div>
-
-<p>The second criterion says that the two Entities present aspects of
-the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-401-Frame" class="MathJax"><nobr><span id="MathJax-Span-7453" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7454" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7455" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7456" class="mi">b</span><span id="MathJax-Span-7457" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7458" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7459" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-401" type="math/tex">obj_1</script> and
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-402-Frame" class="MathJax"><nobr><span id="MathJax-Span-7460" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7461" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7462" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7463" class="mi">b</span><span id="MathJax-Span-7464" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7465" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7466" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-402" type="math/tex">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-403-Frame" class="MathJax"><nobr><span id="MathJax-Span-7467" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7468" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7469" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7470" class="mi">b</span><span id="MathJax-Span-7471" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7472" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7473" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-403" type="math/tex">obj_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-404-Frame" class="MathJax"><nobr><span id="MathJax-Span-7474" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7475" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7476" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7477" class="mi">b</span><span id="MathJax-Span-7478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7479" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7480" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-404" type="math/tex">obj_1</script> to have more defined attributes than
-<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-405-Frame" class="MathJax"><nobr><span id="MathJax-Span-7481" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7482" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7483" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7484" class="mi">b</span><span id="MathJax-Span-7485" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7486" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7487" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-405" type="math/tex">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-406-Frame" class="MathJax"><nobr><span id="MathJax-Span-7488" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7489" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7490" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7491" class="mi">b</span><span id="MathJax-Span-7492" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7493" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7494" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-406" type="math/tex">obj_2</script>.
-</p>
-
-</section>
-<section id="alternate">
-
-<h4><span class="secno">4.4.13 </span> Alternate </h4>
-
-<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-407-Frame" class="MathJax"><nobr><span id="MathJax-Span-7495" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7496" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7497" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7498" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7499" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7500" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7501" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7502" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7504" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7505" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7506" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7507" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-407" type="math/tex">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing. The two entities may or may not overlap in time.
-</p>
-<div data-title="Formalism 26 (rule_26)" data-count="26" id="rule_26" class="formalism"><div class="ruleTitle"><a href="#rule_26" class="internalDFN">Formalism 26 (rule_26)</a></div>
- <p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-408-Frame" class="MathJax"><nobr><span id="MathJax-Span-7508" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7509" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7510" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7511" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7512" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7513" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7514" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7515" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7517" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7518" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7519" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7520" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7521" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7522" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7523" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7524" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7525" class="mo">(</span><span id="MathJax-Span-7526" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7527" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7528" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7529" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7530" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7531" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7532" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7533" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-408" type="math/tex">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
-<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-409-Frame" class="MathJax"><nobr><span id="MathJax-Span-7534" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7535" class="mrow"><span id="MathJax-Span-7536" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7537" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7538" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-409" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-410-Frame" class="MathJax"><nobr><span id="MathJax-Span-7539" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7540" class="mrow"><span id="MathJax-Span-7541" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7542" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7543" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-410" type="math/tex">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-411-Frame" class="MathJax"><nobr><span id="MathJax-Span-7544" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7545" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7546" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7547" class="mi">n</span><span id="MathJax-Span-7548" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7550" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7551" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7552" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7553" class="mo">(</span><span id="MathJax-Span-7554" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7555" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7556" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7557" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-411" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-412-Frame" class="MathJax"><nobr><span id="MathJax-Span-7558" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7559" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7560" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7561" class="mi">n</span><span id="MathJax-Span-7562" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7563" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7564" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7565" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7566" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7567" class="mo">(</span><span id="MathJax-Span-7568" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7569" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7570" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7571" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-412" type="math/tex">ent_2 = \rho(e_2)</script>.
-</li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-413-Frame" class="MathJax"><nobr><span id="MathJax-Span-7572" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7573" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7575" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7576" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7577" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7578" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7579" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7580" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7581" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7582" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7583" class="mi">n</span><span id="MathJax-Span-7584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7585" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7586" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7587" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7588" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7589" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7590" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7591" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7592" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7593" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7594" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7595" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7596" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7597" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7598" class="mi">n</span><span id="MathJax-Span-7599" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7600" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7601" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7602" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-413" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>
-</li></ol>
-</div>
-
-
-</section>
-
-
-<section id="membership">
-
-<h4><span class="secno">4.4.14 </span> Membership </h4>
-
-<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-414-Frame" class="MathJax"><nobr><span id="MathJax-Span-7603" class="math"><span style="display: inline-block; position: relative; width: 84px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.507em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7604" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7605" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7606" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7607" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7608" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7610" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7611" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7612" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7613" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-414" type="math/tex">hadMember</script> relation relates a collection to an element of the collection.
-</p>
-<div data-title="Formalism 27 (rule_27)" data-count="27" id="rule_27" class="formalism"><div class="ruleTitle"><a href="#rule_27" class="internalDFN">Formalism 27 (rule_27)</a></div>
- <p>
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-415-Frame" class="MathJax"><nobr><span id="MathJax-Span-7614" class="math"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7615" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7616" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7617" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7618" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7619" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7620" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7621" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7622" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7623" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7625" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7626" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7628" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7629" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7630" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7631" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7632" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7633" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-415" type="math/tex">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
-<ol>
-<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-416-Frame" class="MathJax"><nobr><span id="MathJax-Span-7634" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7635" class="mrow"><span id="MathJax-Span-7636" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7637" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7638" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-416" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-417-Frame" class="MathJax"><nobr><span id="MathJax-Span-7639" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7640" class="mrow"><span id="MathJax-Span-7641" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7642" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7643" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-417" type="math/tex">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-418-Frame" class="MathJax"><nobr><span id="MathJax-Span-7644" class="math"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.496em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7645" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7647" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7649" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7650" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7651" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7652" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7653" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7654" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7655" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7656" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7657" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7658" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7659" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7660" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7661" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7663" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7664" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7665" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7666" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-418" type="math/tex">coll
- = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-419-Frame" class="MathJax"><nobr><span id="MathJax-Span-7667" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7668" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7670" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7672" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7673" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7674" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7675" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7676" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7677" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7678" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7679" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7680" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7681" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7682" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7683" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7684" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7685" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-419" type="math/tex">ent = \rho(e) \in Entities</script>.
-</li>
-<li>TODO
-</li></ol>
-</div>
-<div class="note"><div class="note-title"><span>Note</span></div><div class="">
- <p>Additional constraints needed above to refer to (not yet defined)
-collection structure of entities/things.</p>
- </div></div>
-
-
-</section>
-
-</section>
-
- <section id="auxiliary-formulas">
- <h3><span class="secno">4.5 </span>Auxiliary formulas</h3>
-
- <p>In this section, we define the semantics of additional formulas
- concerning ordering, null values, and typing. These are used in the
- logical versions of constraints.</p>
-
- <section id="equals">
- <h4><span class="secno">4.5.1 </span>Equals</h4>
- <p>As usual, an equality formula means that two expressions denote
- the same value. Identifiers always denote <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-420-Frame" class="MathJax"><nobr><span id="MathJax-Span-7686" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7687" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7688" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7689" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7690" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7691" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7692" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7693" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7694" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-420" type="math/tex">Objects</script>.</p>
- <div data-title="Formalism 28 (equality)" data-count="28" class="formalism" id="equality"><div class="ruleTitle"><a href="#equality" class="internalDFN">Formalism 28 (equality)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-421-Frame" class="MathJax"><nobr><span id="MathJax-Span-7695" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7696" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7697" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7698" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7699" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7700" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7701" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7702" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7703" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-421" type="math/tex">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-422-Frame" class="MathJax"><nobr><span id="MathJax-Span-7704" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7705" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7706" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7707" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7708" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7709" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7710" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7711" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7712" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7713" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7714" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-422" type="math/tex">\rho(x) =
- \rho(y)</script>.</p>
- </div>
- </section>
- <section id="precedes-and-strictly-precedes">
- <h4><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</h4>
- <p>The precedes relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-423-Frame" class="MathJax"><nobr><span id="MathJax-Span-7715" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7716" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7717" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7718" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7719" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.997em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-423" type="math/tex">x \preceq y</script> holds between two events, one taking
- place before (or simultaneously with) another. Since the
- reference semantics assumes that times are linearly ordered and
- event times are
- mapped to a single time line, this amounts to
- comparing the event times. The semantics of strictly precedes (<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-424-Frame" class="MathJax"><nobr><span id="MathJax-Span-7720" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.863em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7721" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7722" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7723" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7724" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.915em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-424" type="math/tex">x
- \prec y</script> is similar, only <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-425-Frame" class="MathJax"><nobr><span id="MathJax-Span-7725" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7726" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7727" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-425" type="math/tex">x</script> must take place strictly before <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-426-Frame" class="MathJax"><nobr><span id="MathJax-Span-7728" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.55em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7729" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7730" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-426" type="math/tex">y</script>).</p>
- <div data-title="Formalism 29 (precedes)" data-count="29" class="formalism" id="precedes"><div class="ruleTitle"><a href="#precedes" class="internalDFN">Formalism 29 (precedes)</a></div>
- <ol>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-427-Frame" class="MathJax"><nobr><span id="MathJax-Span-7731" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7732" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7733" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7735" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7736" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7737" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7738" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7739" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-427" type="math/tex">W,\rho \models x \preceq y</script> holds if and only if
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-428-Frame" class="MathJax"><nobr><span id="MathJax-Span-7740" class="math"><span style="display: inline-block; position: relative; width: 131px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7741" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7742" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7743" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7744" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7745" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7747" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7748" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7749" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7750" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7751" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7752" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7753" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7754" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7755" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7756" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7757" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-428" type="math/tex">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-429-Frame" class="MathJax"><nobr><span id="MathJax-Span-7758" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7759" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7762" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7763" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7764" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7765" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7766" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7767" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7768" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7769" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7770" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7772" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7773" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7774" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7775" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7776" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7777" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7778" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7779" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7780" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-429" type="math/tex">time(\rho(x)) \leq time(\rho(y))</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-430-Frame" class="MathJax"><nobr><span id="MathJax-Span-7781" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7782" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7783" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7785" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7786" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7787" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7788" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7789" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-430" type="math/tex">W,\rho \models x \prec y</script> holds if and only if
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-431-Frame" class="MathJax"><nobr><span id="MathJax-Span-7790" class="math"><span style="display: inline-block; position: relative; width: 131px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7791" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7792" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7793" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7794" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7795" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7796" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7797" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7798" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7799" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7800" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7801" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7802" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7803" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7804" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7805" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7807" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-431" type="math/tex">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-432-Frame" class="MathJax"><nobr><span id="MathJax-Span-7808" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7809" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7812" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7813" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7814" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7815" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7816" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7817" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7818" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7819" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7820" class="mo"><</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7822" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7823" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7824" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7825" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7826" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7827" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7828" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7829" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7830" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-432" type="math/tex">time(\rho(x)) < time(\rho(y))</script>.</li>
- </ol>
- </div>
- </section>
-
- <section id="notnull">
- <h4><span class="secno">4.5.3 </span>notNull</h4>
- <p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-433-Frame" class="MathJax"><nobr><span id="MathJax-Span-7831" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.512em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7832" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7833" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7834" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7836" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7837" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7838" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7839" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7840" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7841" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7842" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-433" type="math/tex">notNull(x)</script> formula is used to specify that a value may not
- be the null value <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-434-Frame" class="MathJax"><nobr><span id="MathJax-Span-7843" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.745em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7844" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-7845" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.833em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-434" type="math/tex">\bot</script>. The symbol <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-435-Frame" class="MathJax"><nobr><span id="MathJax-Span-7846" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7847" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-7848" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-435" type="math/tex">-</script> always denotes the null
- value (i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-436-Frame" class="MathJax"><nobr><span id="MathJax-Span-7849" class="math"><span style="display: inline-block; position: relative; width: 66px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7850" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7851" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7852" class="mo">(</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7853" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7854" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7855" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7856" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-436" type="math/tex">\rho(-) = \bot</script>).
- </p><div data-title="Formalism 30 (notNull)" data-count="30" class="formalism" id="notNull"><div class="ruleTitle"><a href="#notNull" class="internalDFN">Formalism 30 (notNull)</a></div>
- <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-437-Frame" class="MathJax"><nobr><span id="MathJax-Span-7857" class="math"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7858" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7859" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7860" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7861" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7862" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7863" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7864" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7865" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7866" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7867" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7868" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7869" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7870" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7871" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7872" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-437" type="math/tex">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-438-Frame" class="MathJax"><nobr><span id="MathJax-Span-7873" class="math"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.901em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7874" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7875" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7876" class="mo">≠</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7877" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-438" type="math/tex">e \neq
- \bot</script>.
- </p>
- </div>
-
- </section>
-
- <section id="typeof">
- <h4><span class="secno">4.5.4 </span>typeOf</h4>
-
- <p>The typing formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-439-Frame" class="MathJax"><nobr><span id="MathJax-Span-7878" class="math"><span style="display: inline-block; position: relative; width: 80px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7879" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7880" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7881" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7882" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7883" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7884" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7885" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7886" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7887" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7888" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7890" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-439" type="math/tex">typeOf(x,t)</script> constrains the type of the value of
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-440-Frame" class="MathJax"><nobr><span id="MathJax-Span-7891" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7892" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7893" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-440" type="math/tex">x</script>. </p>
-
- <div data-title="Formalism 31 (typeOf)" data-count="31" class="formalism" id="typeOf"><div class="ruleTitle"><a href="#typeOf" class="internalDFN">Formalism 31 (typeOf)</a></div>
- <ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-441-Frame" class="MathJax"><nobr><span id="MathJax-Span-7894" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7895" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7896" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7897" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7898" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7899" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7900" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7901" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7902" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7903" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7904" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7905" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7906" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7907" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7908" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7909" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7910" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7911" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7912" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7914" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7915" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-441" type="math/tex">W,\rho\models typeOf(e,entity)</script> holds if and only if
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-442-Frame" class="MathJax"><nobr><span id="MathJax-Span-7916" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7917" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7918" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7919" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7920" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7921" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7922" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7923" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7924" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7925" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7926" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7927" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7928" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7929" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7930" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-442" type="math/tex">\rho(e) \in Entities</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-443-Frame" class="MathJax"><nobr><span id="MathJax-Span-7931" class="math"><span style="display: inline-block; position: relative; width: 181px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7932" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7933" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7934" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7935" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7936" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7938" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7939" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7940" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7941" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7942" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7943" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7944" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7945" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7946" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7947" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7949" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7950" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7951" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7953" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7954" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-443" type="math/tex">W,\rho\models typeOf(a,activity)</script> holds if and only if
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-444-Frame" class="MathJax"><nobr><span id="MathJax-Span-7955" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7956" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7957" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7958" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7959" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7960" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7961" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7962" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7963" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7965" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7966" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7967" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7968" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7969" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7970" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7971" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-444" type="math/tex">\rho(a) \in Activities</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-445-Frame" class="MathJax"><nobr><span id="MathJax-Span-7972" class="math"><span style="display: inline-block; position: relative; width: 176px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7973" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7974" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7975" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7976" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7977" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7978" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7979" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7980" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7981" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7982" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7983" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7984" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7985" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7986" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7987" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7988" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7989" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7990" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7991" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7993" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-445" type="math/tex">W,\rho\models typeOf(ag,agent)</script> holds if and only if
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-446-Frame" class="MathJax"><nobr><span id="MathJax-Span-7994" class="math"><span style="display: inline-block; position: relative; width: 105px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7995" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7996" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7997" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7998" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7999" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8000" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8001" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8002" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8003" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8004" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8005" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8006" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8007" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-446" type="math/tex">\rho(ag) \in Agents</script>.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-447-Frame" class="MathJax"><nobr><span id="MathJax-Span-8008" class="math"><span style="display: inline-block; position: relative; width: 249px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8009" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8010" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8011" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8012" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8013" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8015" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8016" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8017" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8018" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8019" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8020" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8021" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8022" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8023" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8024" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8025" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8026" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8027" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8028" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8029" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8030" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8031" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8032" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8033" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8034" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8035" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8036" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8037" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8038" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-447" type="math/tex">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
- TODO.</li>
- <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-448-Frame" class="MathJax"><nobr><span id="MathJax-Span-8039" class="math"><span style="display: inline-block; position: relative; width: 293px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8040" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8041" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8043" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8044" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8046" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8047" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8048" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8049" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8050" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8051" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8052" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8053" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8054" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8055" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8056" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8057" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8058" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8059" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8060" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8061" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8063" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8064" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8065" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8066" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8067" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8069" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8070" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8072" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8073" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8074" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-448" type="math/tex">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
- TODO.</li>
- </ol>
-
- </div>
-
- <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO Collections</div></div>
-
- </section>
-
- </section>
- </section>
-
-<section id="theory">
-<!--OddPage--><h2><span class="secno">5. </span> Inferences and Constraints </h2>
-
- <p>
- In this section we restate all of the inferences and constraints
- of PROV-CONSTRAINTS in terms of first-order logic. For each, we
- give a proof sketch showing why the inference or constraint is
- sound for reasoning about the reference semantics. We exclude the
- definitional rules in PROV-CONSTRAINTS because they are only
- needed for expanding the abbreviated forms of PROV-N statements to
- the logical formulas used here.</p>
-<section id="inferences">
-<h3><span class="secno">5.1 </span>Inferences</h3>
-
-<div class="inference" number="5" id="communication-generation-use-inference"><div class="ruleTitle"><a href="#communication-generation-use-inference" class="internalDFN">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-449-Frame" class="MathJax"><nobr><span id="MathJax-Span-8075" class="math"><span style="display: inline-block; position: relative; width: 573px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.049em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8076" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8077" class="mtable"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.502em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8078" class="mtd"><span id="MathJax-Span-8079" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8080" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8082" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8083" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8084" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8085" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8086" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8087" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8088" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8089" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8090" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8091" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8092" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8093" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8094" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8095" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8096" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8097" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8098" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8099" class="mtd"><span id="MathJax-Span-8100" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8101" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8102" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8103" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8104" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8105" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8106" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8107" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8108" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8109" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8110" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8111" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8112" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8113" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8114" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8115" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8116" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8117" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8118" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8119" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8120" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8121" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8122" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8123" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8124" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8125" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8126" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8127" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8130" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8131" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8132" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-8133" class="mtd"><span id="MathJax-Span-8134" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8135" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8136" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8137" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8138" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8139" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8140" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8141" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8142" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8143" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8144" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8145" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8146" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8147" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8148" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8149" class="mi">s</span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8181" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8182" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8183" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8184" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8185" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8186" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8187" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8188" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8189" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8190" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8191" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8193" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8194" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8195" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8196" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8197" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8198" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8199" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8200" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8201" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8202" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8203" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8204" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8205" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8207" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8208" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8209" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8210" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8211" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-449" type="math/tex">\begin{array}[t]{l}
-\forall id,a_2,a_1,attrs.~
-\\
-\qquad wasInformedBy(id,a_2,a_1,attrs)
-\\
-\quad\Rightarrow
-\exists e,gen,t_1,use,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge used(use,a_2,e,t_2,[])
-\end{array}</script></div>
-<div class="inference" number="6" id="generation-use-communication-inference"><div class="ruleTitle"><a href="#generation-use-communication-inference" class="internalDFN">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-450-Frame" class="MathJax"><nobr><span id="MathJax-Span-8212" class="math"><span style="display: inline-block; position: relative; width: 493px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8213" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8214" class="mtable"><span style="display: inline-block; position: relative; width: 28.446em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.446em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8215" class="mtd"><span id="MathJax-Span-8216" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8217" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8218" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8219" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8220" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8221" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8222" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8223" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8224" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8225" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8226" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8227" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8228" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8230" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8231" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8232" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8235" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8236" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8237" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8238" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8239" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8240" class="mi">i</span><span id="MathJax-Span-8241" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8243" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8244" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8245" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8246" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8247" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8248" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8249" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8251" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8252" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8253" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8255" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8256" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8257" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8258" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8259" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8260" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8261" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-8262" class="mtd"><span id="MathJax-Span-8263" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8264" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8265" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8267" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8268" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8269" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8270" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8271" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8272" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8273" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8274" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8276" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8277" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8278" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8279" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8280" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8281" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8282" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8283" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8284" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8285" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8286" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8287" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8288" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8289" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8290" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8292" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8297" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8298" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8299" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8300" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8301" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8302" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8303" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8304" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8305" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8306" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8307" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8308" class="mi">i</span><span id="MathJax-Span-8309" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8310" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8311" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8312" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8313" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8314" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8315" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8316" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8317" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8318" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8319" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8320" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8321" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8322" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8323" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8324" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8325" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8326" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8327" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8328" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8329" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8330" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-8331" class="mtd"><span id="MathJax-Span-8332" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8333" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8334" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8335" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8338" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8339" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8340" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8341" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8342" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8343" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8344" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8345" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8346" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8347" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8348" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8349" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8350" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8351" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8352" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8353" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8354" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8355" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8356" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8357" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8358" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8359" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8362" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8364" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8365" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8366" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8367" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-450" type="math/tex">\begin{array}[t]{l}
-\forall gen,e,a_1,t_1,attrs_1,id_2,a_2,t_2,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(id_2,a_2,e,t_2,attrs_2)
-\\
-\quad\Rightarrow
-\exists id.~wasInformedBy(id,a_2,a_1,[])
-\end{array}</script></div>
-<div class="inference" number="7" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a href="#entity-generation-invalidation-inference" class="internalDFN">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-451-Frame" class="MathJax"><nobr><span id="MathJax-Span-8368" class="math"><span style="display: inline-block; position: relative; width: 693px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.032em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8369" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8370" class="mtable"><span style="display: inline-block; position: relative; width: 40.129em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.485em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 40.129em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8371" class="mtd"><span id="MathJax-Span-8372" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8373" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8374" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8376" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8377" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8379" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8380" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8381" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8382" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.303em; left: 0em;"><span id="MathJax-Span-8383" class="mtd"><span id="MathJax-Span-8384" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8385" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8387" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8388" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8389" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8391" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8392" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8393" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8394" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8395" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8397" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8398" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8399" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8400" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.036em; left: 0em;"><span id="MathJax-Span-8401" class="mtd"><span id="MathJax-Span-8402" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8403" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8404" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8405" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8406" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8408" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8409" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8410" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8411" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8412" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8413" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8414" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8416" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8417" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8418" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8419" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8420" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8421" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8422" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8423" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8424" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8425" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8426" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8428" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8429" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8430" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8431" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8432" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8433" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8434" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8435" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8436" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8437" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8438" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8439" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8441" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8442" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8443" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8444" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8445" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8446" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8447" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8448" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8450" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8451" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8453" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8454" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8455" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8456" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8457" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8458" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8459" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8460" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8461" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8462" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8463" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8464" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8466" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8467" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8468" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8469" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8471" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8472" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8473" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8476" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8477" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8478" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8479" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8480" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8481" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8482" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8483" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8484" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8485" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8486" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8487" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8488" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8489" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8490" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8491" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8492" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8493" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8494" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8495" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8496" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8497" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.99em; vertical-align: -3.071em;"></span></span></nobr></span><script id="MathJax-Element-451" type="math/tex">\begin{array}[t]{l}
-\forall e,attrs.~
-\\
-\qquad entity(e,attrs)
-\\
-\quad\Rightarrow
-\exists gen,a_1,t_1,inv,a_2,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge wasInvalidatedBy(inv,e,a_2,t_2,[])
-\end{array}</script></div>
-<div class="inference" number="8" id="activity-start-end-inference"><div class="ruleTitle"><a href="#activity-start-end-inference" class="internalDFN">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-452-Frame" class="MathJax"><nobr><span id="MathJax-Span-8498" class="math"><span style="display: inline-block; position: relative; width: 716px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.041em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8499" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8500" class="mtable"><span style="display: inline-block; position: relative; width: 41.472em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.494em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 41.472em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8501" class="mtd"><span id="MathJax-Span-8502" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8503" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8504" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8505" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8506" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8507" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8508" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8509" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8510" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8511" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8512" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8513" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8514" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8515" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8517" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8518" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8519" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8520" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.294em; left: 0em;"><span id="MathJax-Span-8521" class="mtd"><span id="MathJax-Span-8522" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8523" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8524" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8525" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8527" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8528" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8529" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8531" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8532" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8533" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8534" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8535" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8537" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8538" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8539" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8541" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8542" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8545" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8546" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8547" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8548" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.045em; left: 0em;"><span id="MathJax-Span-8549" class="mtd"><span id="MathJax-Span-8550" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8551" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8552" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8553" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8554" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8557" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8559" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8560" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8561" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8562" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8563" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8564" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8565" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8566" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8567" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8569" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8570" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8574" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8577" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8578" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8579" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8580" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8581" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8583" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8584" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8585" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8586" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8587" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8590" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8591" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8592" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8593" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8594" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8596" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8597" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8598" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8599" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8600" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8601" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8603" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8604" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8605" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8606" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8607" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8608" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8609" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8613" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8614" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8615" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8616" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8617" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8618" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8619" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8620" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8621" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8622" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8623" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8625" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8626" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8627" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8628" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8630" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8631" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8632" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8633" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8634" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8635" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8636" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8637" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8638" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8639" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8640" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8641" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8642" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8643" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8645" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8646" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8647" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8648" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8649" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.999em; vertical-align: -3.081em;"></span></span></nobr></span><script id="MathJax-Element-452" type="math/tex">\begin{array}[t]{l}
-\forall a,t_1,t_2,attrs.~
-\\
-\qquad activity(a,t_1,t_2,attrs)
-\\
-\quad\Rightarrow
-\exists start,e_1,a_1,end,a_2,e_2.~wasStartedBy(start,a,e_1,a_1,t_1,[]) \wedge wasEndedBy(end,a,e_2,a_2,t_2,[])
-\end{array}</script></div>
-<div class="inference" number="9" id="wasStartedBy-inference"><div class="ruleTitle"><a href="#wasStartedBy-inference" class="internalDFN">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-453-Frame" class="MathJax"><nobr><span id="MathJax-Span-8650" class="math"><span style="display: inline-block; position: relative; width: 352px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.048em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8651" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8652" class="mtable"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8653" class="mtd"><span id="MathJax-Span-8654" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8655" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8656" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8657" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8658" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8659" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8660" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8661" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8662" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8663" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8664" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8665" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8666" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8667" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8668" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8669" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8670" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8672" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8674" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8675" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8676" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8677" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8678" class="mtd"><span id="MathJax-Span-8679" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8680" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8681" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8682" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8683" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8684" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8685" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8686" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8687" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8688" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8689" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8690" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8691" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8692" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8693" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8694" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8695" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8697" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8698" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8699" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8700" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8701" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8702" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8703" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8704" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8705" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8706" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8707" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8708" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8709" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8711" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8712" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8713" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8714" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-8715" class="mtd"><span id="MathJax-Span-8716" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8717" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8718" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8719" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8720" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8721" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8722" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8723" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8724" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8725" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8726" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8727" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8728" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8729" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8730" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8731" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8732" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8733" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8734" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8735" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8736" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8737" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8740" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8741" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8742" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8743" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8744" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8745" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8746" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8747" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8748" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8749" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8750" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8751" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8752" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8753" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8754" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8755" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8757" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8758" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8759" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8760" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8761" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8762" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.007em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-453" type="math/tex">\begin{array}[t]{l}
-\forall id,a,e_1,a_1,t,attrs.~
-\\
-\qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
-\\
-\quad\Rightarrow
-\exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
-\end{array}</script></div>
-<div class="inference" number="10" id="wasEndedBy-inference"><div class="ruleTitle"><a href="#wasEndedBy-inference" class="internalDFN">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-454-Frame" class="MathJax"><nobr><span id="MathJax-Span-8763" class="math"><span style="display: inline-block; position: relative; width: 352px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.048em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8764" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8765" class="mtable"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8766" class="mtd"><span id="MathJax-Span-8767" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8768" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8769" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8770" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8771" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8772" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8773" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8774" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8775" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8776" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8777" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8778" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8779" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8780" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8781" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8783" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8784" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8785" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8786" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8787" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8788" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8789" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8790" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8791" class="mtd"><span id="MathJax-Span-8792" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8793" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8794" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8795" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8796" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8797" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8798" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8799" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8800" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8801" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8802" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8803" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8804" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8805" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8806" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8807" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8808" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8809" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8810" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8811" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8812" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8813" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8814" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8815" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8816" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8817" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8818" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8819" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8820" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8822" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8823" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8824" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8825" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-8826" class="mtd"><span id="MathJax-Span-8827" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8828" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8829" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8830" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8831" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8832" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8833" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8834" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8835" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8837" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8838" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8839" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8840" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8841" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8842" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8843" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8844" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8845" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8846" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8847" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8848" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8849" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8851" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8852" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8853" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8854" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8855" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8856" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8857" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8858" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8859" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8860" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8861" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8862" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8863" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8864" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8865" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8866" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8867" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8869" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8870" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8871" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8872" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8873" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.007em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-454" type="math/tex">\begin{array}[t]{l}
-\forall id,a,e_1,a_1,t,attrs.~
-\\
-\qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
-\\
-\quad\Rightarrow
-\exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
-\end{array}</script></div>
-<div class="inference" number="11" id="derivation-generation-use-inference"><div class="ruleTitle"><a href="#derivation-generation-use-inference" class="internalDFN">Inference 11 (derivation-generation-use-inference)</a></div><p>In this inference, none of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-455-Frame" class="MathJax"><nobr><span id="MathJax-Span-8874" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8875" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8876" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-455" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-456-Frame" class="MathJax"><nobr><span id="MathJax-Span-8877" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8878" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8879" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8880" class="mi">e</span><span id="MathJax-Span-8881" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8882" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8883" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-456" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-457-Frame" class="MathJax"><nobr><span id="MathJax-Span-8884" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8885" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8886" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8887" class="mi">s</span><span id="MathJax-Span-8888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8889" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8890" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-457" type="math/tex">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-458-Frame" class="MathJax"><nobr><span id="MathJax-Span-8891" class="math"><span style="display: inline-block; position: relative; width: 690px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8892" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8893" class="mtable"><span style="display: inline-block; position: relative; width: 39.953em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 39.953em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8894" class="mtd"><span id="MathJax-Span-8895" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8896" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8897" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8898" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8899" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8900" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8901" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8902" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8903" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8904" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8905" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8906" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8907" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8908" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8909" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8910" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8911" class="mi">e</span><span id="MathJax-Span-8912" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8913" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8914" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8915" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8916" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8917" class="mi">s</span><span id="MathJax-Span-8918" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8919" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8920" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8921" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8922" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8923" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8924" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8925" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8926" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8927" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8928" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-8929" class="mtd"><span id="MathJax-Span-8930" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8931" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8932" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8933" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8934" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8935" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8936" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8937" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8938" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8939" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8940" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8941" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8942" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8943" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8944" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8945" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8946" class="mi">N<span style="display: inline-block; overflow: hidden; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8997" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8998" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8999" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9000" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9001" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9002" class="mi">e</span><span id="MathJax-Span-9003" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9004" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9005" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9007" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9008" class="mi">s</span><span id="MathJax-Span-9009" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9010" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9011" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9012" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9013" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9015" class="mi">t<span style="display: inline-block; overflow: hidden; 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position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9025" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9026" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); 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font-style: italic;" id="MathJax-Span-9064" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9065" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9066" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9069" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9070" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9071" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9072" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9073" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9074" class="mi">e</span><span id="MathJax-Span-9075" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9076" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9077" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9078" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9080" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9081" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9083" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9086" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9088" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9089" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9090" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9091" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-458" type="math/tex">\begin{array}[t]{l}
-\forall id,e_2,e_1,a,gen_2,use_1,attrs.~
-\\
-\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(id,e_2,e_1,a,gen_2,use_1,attrs)
-\\
-\quad\Rightarrow
-\exists t_1,t_2.~used(use_1,a,e_1,t_1,[]) \wedge wasGeneratedBy(gen_2,e_2,a,t_2,[])
-\end{array}</script></div>
-<div class="inference" number="12" id="revision-is-alternate-inference"><div class="ruleTitle"><a href="#revision-is-alternate-inference" class="internalDFN">Inference 12 (revision-is-alternate-inference)</a></div><p>In this inference, any of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-459-Frame" class="MathJax"><nobr><span id="MathJax-Span-9092" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9093" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9094" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-459" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-460-Frame" class="MathJax"><nobr><span id="MathJax-Span-9095" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9096" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9097" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9098" class="mi">e</span><span id="MathJax-Span-9099" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9100" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9101" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-460" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-461-Frame" class="MathJax"><nobr><span id="MathJax-Span-9102" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9103" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9104" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9105" class="mi">s</span><span id="MathJax-Span-9106" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9107" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9108" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-461" type="math/tex">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-462-Frame" class="MathJax"><nobr><span id="MathJax-Span-9109" class="math"><span style="display: inline-block; position: relative; width: 517px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9110" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9111" class="mtable"><span style="display: inline-block; position: relative; width: 29.848em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 29.848em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9112" class="mtd"><span id="MathJax-Span-9113" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9114" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9115" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9116" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9117" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9118" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9119" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9120" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9121" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9122" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9123" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9124" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9126" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9127" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9128" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9129" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9130" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9131" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9132" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-9133" class="mtd"><span id="MathJax-Span-9134" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9135" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9136" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9137" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9138" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9139" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9140" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9141" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9142" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9143" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9145" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9146" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9147" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9148" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9149" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9150" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9151" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9152" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9153" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9154" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9155" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9156" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9157" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9158" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9159" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9160" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9161" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9162" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9163" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9164" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9165" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9166" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9167" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9168" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9169" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9170" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9171" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9172" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9173" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9175" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9176" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9177" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9178" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9179" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9180" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9181" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9182" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9183" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9184" class="mi">R</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9185" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9186" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9187" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9188" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9189" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9190" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9191" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9192" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9193" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9194" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-9195" class="mtd"><span id="MathJax-Span-9196" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9197" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9198" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9199" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9200" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9203" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9204" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9207" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9208" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9209" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9210" class="mo">(</span><span id="MathJax-Span-9211" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9212" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9213" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9214" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9215" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9216" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9217" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9218" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-462" type="math/tex">\begin{array}[t]{l}
-\forall id,e_1,e_2,a,g,u.~
-\\
-\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,[prov:type = prov:Revision]))
-\\
-\quad\Rightarrow
-alternateOf(e_2,e_1)
-\end{array}</script></div>
-<div class="inference" number="13" id="attribution-inference"><div class="ruleTitle"><a href="#attribution-inference" class="internalDFN">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-463-Frame" class="MathJax"><nobr><span id="MathJax-Span-9219" class="math"><span style="display: inline-block; position: relative; width: 691px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9220" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9221" class="mtable"><span style="display: inline-block; position: relative; width: 40.012em; height: 0px;"><span style="position: absolute; clip: rect(3.719em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 40.012em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9222" class="mtd"><span id="MathJax-Span-9223" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9224" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9226" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9228" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9229" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9230" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9231" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9232" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9233" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9234" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9235" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9236" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9237" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9238" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9239" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9240" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-9241" class="mtd"><span id="MathJax-Span-9242" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9243" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9244" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9245" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9246" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9247" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9250" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9251" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9252" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9253" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9255" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9256" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9257" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9258" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9259" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9262" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9263" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9264" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9265" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9267" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9268" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9269" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9272" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9273" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9274" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-9275" class="mtd"><span id="MathJax-Span-9276" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9277" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9278" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9279" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9280" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9281" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9282" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9283" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9284" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9285" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9286" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9287" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9288" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9290" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9291" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9292" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9294" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9295" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9296" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9297" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9298" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9299" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9300" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9301" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9302" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9303" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9304" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9305" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9306" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9307" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9308" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9309" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9310" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9311" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9312" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9315" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9316" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9317" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9318" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9319" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9320" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9321" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9322" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9323" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9324" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9325" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-9326" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-9327" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9328" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9329" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9330" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9331" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9332" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9333" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9334" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9335" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9336" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9338" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9339" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9340" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9341" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9342" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9343" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9346" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9347" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9348" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9349" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9350" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9351" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9353" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9354" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9355" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9356" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9357" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9358" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9359" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9360" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9361" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-463" type="math/tex">\begin{array}[t]{l}
-\forall att,e,ag,attrs.~
-\\
-\qquad wasAttributedTo(att,e,ag,attrs)
-\\
-\quad\Rightarrow
-\exists a,t,gen,assoc,pl.~wasGeneratedBy(gen,e,a,t,[]) \wedge wasAssociatedWith(assoc,a,ag,pl,[])
-\end{array}</script></div>
-<div class="inference" number="14" id="delegation-inference"><div class="ruleTitle"><a href="#delegation-inference" class="internalDFN">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-464-Frame" class="MathJax"><nobr><span id="MathJax-Span-9362" class="math"><span style="display: inline-block; position: relative; width: 722px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.21em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9363" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9364" class="mtable"><span style="display: inline-block; position: relative; width: 41.822em; height: 0px;"><span style="position: absolute; clip: rect(3.815em, 1000em, 7.838em, -0.526em); top: -4.673em; left: 0em;"><span style="display: inline-block; position: relative; width: 41.822em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9365" class="mtd"><span id="MathJax-Span-9366" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9367" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9368" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9369" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9370" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9371" class="mi">a</span><span id="MathJax-Span-9372" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9373" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9374" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9376" class="mi">a</span><span id="MathJax-Span-9377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9378" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9380" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9381" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9382" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9384" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9385" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9386" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9387" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9388" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9389" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-9390" class="mtd"><span id="MathJax-Span-9391" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9392" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9394" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9395" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9396" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9397" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9398" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9399" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9400" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9401" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9402" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9403" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9404" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9405" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9406" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9407" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9408" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9409" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9410" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9411" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9412" class="mi">a</span><span id="MathJax-Span-9413" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9414" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9415" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9416" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9417" class="mi">a</span><span id="MathJax-Span-9418" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9419" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9420" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9421" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9422" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9423" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9425" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9427" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9428" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9429" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-9430" class="mtd"><span id="MathJax-Span-9431" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9432" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9433" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9434" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9435" class="mi">i</span><span id="MathJax-Span-9436" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9437" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9438" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9439" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9440" class="mi">p</span><span id="MathJax-Span-9441" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9442" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9443" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9444" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9445" class="mi">i</span><span id="MathJax-Span-9446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9447" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9448" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9450" class="mi">p</span><span id="MathJax-Span-9451" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9452" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9453" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9454" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9455" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9456" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9457" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9458" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9459" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9460" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9461" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9462" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9463" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9466" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9468" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9469" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9470" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9472" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9473" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9474" class="mi">i</span><span id="MathJax-Span-9475" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9476" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9477" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9478" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9479" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9481" class="mi">a</span><span id="MathJax-Span-9482" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9483" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9484" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9485" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9486" class="mi">p</span><span id="MathJax-Span-9487" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9488" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9489" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9490" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9491" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9492" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9493" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-9494" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-9495" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9496" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9497" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9498" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9499" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9500" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9501" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9502" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9504" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9505" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9506" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9507" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9508" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9509" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9511" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9513" class="mi">i</span><span id="MathJax-Span-9514" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9515" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9516" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9517" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9518" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9519" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9520" class="mi">a</span><span id="MathJax-Span-9521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9522" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9523" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9524" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9525" class="mi">p</span><span id="MathJax-Span-9526" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9527" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9528" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9529" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9530" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9531" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9532" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.18em; vertical-align: -3.262em;"></span></span></nobr></span><script id="MathJax-Element-464" type="math/tex">\begin{array}[t]{l}
-\forall id,ag_1,ag_2,a,attrs.~
-\\
-\qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
-\\
-\quad\Rightarrow
-\exists id_1,pl_1,id_2,pl_2.~wasAssociatedWith(id_1,a,ag_1,pl_1,[]) \wedge wasAssociatedWith(id_2,a,ag_2,pl_2,[])
-\end{array}</script></div>
-<div class="inference" number="15" id="influence-inference"><div class="ruleTitle"><a href="#influence-inference" class="internalDFN">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-465-Frame" class="MathJax"><nobr><span id="MathJax-Span-9533" class="math"><span style="display: inline-block; position: relative; width: 271px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.04em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9534" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9535" class="mtable"><span style="display: inline-block; position: relative; width: 15.479em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.493em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.479em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9536" class="mtd"><span id="MathJax-Span-9537" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9538" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9539" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9540" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9541" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9542" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9543" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9544" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9545" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9547" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9548" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9550" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9551" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9552" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9553" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9554" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-9555" class="mtd"><span id="MathJax-Span-9556" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9557" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9558" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9560" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9561" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9562" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9563" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9564" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9565" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9566" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9567" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9569" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9570" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9571" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9572" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9573" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9574" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9575" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9576" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9577" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9578" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9579" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9581" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9584" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9585" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9586" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9587" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.043em; left: 0em;"><span id="MathJax-Span-9588" class="mtd"><span id="MathJax-Span-9589" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9590" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9591" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9592" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9593" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9594" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9595" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9596" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9597" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9598" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9599" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9602" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9603" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9604" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9605" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9606" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9607" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9608" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9609" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9610" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9611" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9612" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9613" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9614" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9615" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9616" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9618" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9619" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9620" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.998em; vertical-align: -3.08em;"></span></span></nobr></span><script id="MathJax-Element-465" type="math/tex">\begin{array}[t]{l}
-\forall id,e,a,t,attrs.~
-\\
-\qquad wasGeneratedBy(id,e,a,t,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,e,a,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-466-Frame" class="MathJax"><nobr><span id="MathJax-Span-9621" class="math"><span style="display: inline-block; position: relative; width: 263px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.011em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9622" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9623" class="mtable"><span style="display: inline-block; position: relative; width: 15.012em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.464em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.012em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9624" class="mtd"><span id="MathJax-Span-9625" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9626" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9627" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9628" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9629" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9630" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9631" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9632" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9633" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9634" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9635" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9636" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9637" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9638" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9639" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9640" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9641" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9642" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-9643" class="mtd"><span id="MathJax-Span-9644" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9645" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9646" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9647" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9648" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9649" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9650" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9651" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9652" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9653" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9654" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9656" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9657" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9659" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9663" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9664" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9665" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.014em; left: 0em;"><span id="MathJax-Span-9666" class="mtd"><span id="MathJax-Span-9667" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9668" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9669" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9670" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9672" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9673" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9674" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9675" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9676" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9677" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9678" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9679" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9680" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9681" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9682" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9683" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9684" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9685" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9686" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9687" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9688" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9689" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9690" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9691" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9693" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9694" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9695" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9696" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9697" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9698" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.967em; vertical-align: -3.049em;"></span></span></nobr></span><script id="MathJax-Element-466" type="math/tex">\begin{array}[t]{l}
-\forall id,a,e,t,attrs.~
-\\
-\qquad used(id,a,e,t,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,a,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-467-Frame" class="MathJax"><nobr><span id="MathJax-Span-9699" class="math"><span style="display: inline-block; position: relative; width: 280px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9700" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9701" class="mtable"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9702" class="mtd"><span id="MathJax-Span-9703" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9704" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9705" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9706" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9707" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9708" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9709" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9710" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9711" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9712" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9713" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9714" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9715" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9716" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9719" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9720" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9721" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9722" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9723" class="mtd"><span id="MathJax-Span-9724" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9725" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9726" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9727" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9728" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9729" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9730" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9731" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9732" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9733" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9734" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9735" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9736" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9737" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9738" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9739" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9740" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9741" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9742" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9743" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9744" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9745" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9746" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9747" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9748" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9749" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9750" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9751" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9753" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9754" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9755" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9756" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-9757" class="mtd"><span id="MathJax-Span-9758" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9759" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9760" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9761" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9762" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9763" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9764" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9765" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9766" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9767" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9768" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9769" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9770" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9771" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9772" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9773" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9774" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9775" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9776" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9778" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9779" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9780" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9781" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9782" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9783" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9785" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9786" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9787" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9788" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9789" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9790" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9791" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9792" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9793" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-467" type="math/tex">\begin{array}[t]{l}
-\forall id,a_2,a_1,attrs.~
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height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9806" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9807" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9808" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9809" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9810" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9811" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9812" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9813" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9814" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9815" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9819" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9820" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9821" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9822" class="mtd"><span id="MathJax-Span-9823" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9824" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9825" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9826" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9827" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9828" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9829" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9830" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9831" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9832" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9833" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9834" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9835" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9836" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9837" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9838" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9839" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9840" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9841" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9842" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9843" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9844" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9845" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9846" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9847" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9848" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9849" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9852" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9853" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9854" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9856" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9857" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9858" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-9859" class="mtd"><span id="MathJax-Span-9860" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9861" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9862" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9863" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9864" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9865" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9866" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9867" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9868" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9869" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9870" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9871" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9872" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9873" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9874" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9875" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9876" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9877" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9878" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9879" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9880" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9881" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9882" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9883" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9884" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9886" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9887" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9888" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9890" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9891" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9892" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9893" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-468" type="math/tex">\begin{array}[t]{l}
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-\\
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-wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-469-Frame" class="MathJax"><nobr><span id="MathJax-Span-9894" class="math"><span style="display: inline-block; position: relative; width: 274px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.049em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9895" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9896" class="mtable"><span style="display: inline-block; position: relative; width: 15.654em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.502em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.654em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9897" class="mtd"><span id="MathJax-Span-9898" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9899" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9900" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9901" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9902" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9903" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9904" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9905" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9906" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9907" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9908" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9909" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9910" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9911" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9912" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9914" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9917" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9918" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9919" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9920" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9921" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9922" class="mtd"><span id="MathJax-Span-9923" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9924" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9925" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9926" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9927" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9928" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9929" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9930" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9931" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9932" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9933" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9934" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9936" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9937" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9938" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9939" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9940" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9941" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9942" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9943" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9944" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9946" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9948" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9949" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9950" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9951" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9954" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9955" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9956" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-9957" class="mtd"><span id="MathJax-Span-9958" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9959" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9960" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9961" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9962" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9963" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9965" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9966" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9967" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9968" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9969" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9970" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9971" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9978" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9979" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9980" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9981" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9982" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9983" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9984" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9985" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9987" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9989" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9990" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9991" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-469" type="math/tex">\begin{array}[t]{l}
-\forall id,a_2,e,a_1,t,attrs.~
-\\
-\qquad wasEndedBy(id,a_2,e,a_1,t,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,a_2,e,attrs)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-470-Frame" class="MathJax"><nobr><span id="MathJax-Span-9992" class="math"><span style="display: inline-block; position: relative; width: 278px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.04em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9993" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9994" class="mtable"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.493em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9995" class="mtd"><span id="MathJax-Span-9996" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9997" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9998" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10000" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10001" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10002" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10003" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10004" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10007" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10010" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10011" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10012" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10013" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-10014" class="mtd"><span id="MathJax-Span-10015" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10016" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10017" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10018" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10019" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10020" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10021" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10022" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10023" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10024" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10025" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10026" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10027" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10029" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10030" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10031" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10032" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10033" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10034" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10035" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10036" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10037" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10038" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10039" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10040" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10041" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10043" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; 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height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10170" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10171" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10172" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10173" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10174" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10175" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10177" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10178" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10179" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10180" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10181" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10182" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10183" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10184" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10185" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10186" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10187" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10188" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10189" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-471" type="math/tex">\begin{array}[t]{l}
-\forall id,e_2,e_1,a,g,u,attrs.~
-\\
-\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,e_2,e_1,attrs)
-\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-472-Frame" class="MathJax"><nobr><span id="MathJax-Span-10190" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10191" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10192" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-472" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-473-Frame" class="MathJax"><nobr><span id="MathJax-Span-10193" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10194" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10195" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-473" type="math/tex">g</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-474-Frame" class="MathJax"><nobr><span id="MathJax-Span-10196" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10197" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10198" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-474" type="math/tex">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-475-Frame" class="MathJax"><nobr><span id="MathJax-Span-10199" class="math"><span style="display: inline-block; position: relative; width: 272px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10200" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10201" class="mtable"><span style="display: inline-block; position: relative; width: 15.537em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.537em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10202" class="mtd"><span id="MathJax-Span-10203" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10204" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10205" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10206" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10207" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10208" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10209" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10210" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10211" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10212" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10213" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10215" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10216" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10217" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10218" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10219" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-10220" class="mtd"><span id="MathJax-Span-10221" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10222" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10223" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10224" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10225" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10226" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10229" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10230" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10231" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10232" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10234" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10235" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10236" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10237" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10238" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10239" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10240" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10241" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10242" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10243" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10244" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10245" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10247" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10250" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10251" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10252" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-10253" class="mtd"><span id="MathJax-Span-10254" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10255" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10256" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10257" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10258" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10259" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10260" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10261" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10262" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10263" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10264" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10265" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10266" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10267" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10268" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10269" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10270" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10271" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10272" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10273" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10274" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10276" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10279" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10280" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10281" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10282" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10284" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10285" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10286" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-475" type="math/tex">\begin{array}[t]{l}
-\forall id,e,ag,attrs.~
-\\
-\qquad wasAttributedTo(id,e,ag,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,e,ag,attrs)
-\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-476-Frame" class="MathJax"><nobr><span id="MathJax-Span-10287" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10288" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10289" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10290" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-476" type="math/tex">pl</script> may be a placeholder -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-477-Frame" class="MathJax"><nobr><span id="MathJax-Span-10291" class="math"><span style="display: inline-block; position: relative; width: 307px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10292" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10293" class="mtable"><span style="display: inline-block; position: relative; width: 17.582em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.582em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10294" class="mtd"><span id="MathJax-Span-10295" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10296" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10297" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10298" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10300" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10301" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10302" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10303" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10305" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10306" class="mi">l<span style="display: inline-block; 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height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-477" type="math/tex">\begin{array}[t]{l}
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position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10439" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10440" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10441" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10442" class="mi">a</span><span id="MathJax-Span-10443" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10444" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10445" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10446" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10447" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10448" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10449" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10452" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10453" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10454" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-10455" class="mtd"><span id="MathJax-Span-10456" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10457" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10458" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10459" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10460" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10461" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10462" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10463" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10464" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10465" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10466" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10468" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10469" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10470" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10471" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10472" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10473" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10474" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10475" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10476" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10477" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10478" class="mi">a</span><span id="MathJax-Span-10479" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10480" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10481" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10482" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10483" class="mi">a</span><span id="MathJax-Span-10484" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10485" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10486" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10487" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10490" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10491" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10492" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10493" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.18em; vertical-align: -3.262em;"></span></span></nobr></span><script id="MathJax-Element-478" type="math/tex">\begin{array}[t]{l}
-\forall id,ag_2,ag_1,a,attrs.~
-\\
-\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
-\\
-\quad\Rightarrow
-wasInfluencedBy(id,ag_2,ag_1,attrs)
-\end{array}</script></li></ol></div>
-<div class="inference" number="16" id="alternate-reflexive"><div class="ruleTitle"><a href="#alternate-reflexive" class="internalDFN">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-479-Frame" class="MathJax"><nobr><span id="MathJax-Span-10494" class="math"><span style="display: inline-block; position: relative; width: 163px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.966em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10495" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10496" class="mtable"><span style="display: inline-block; position: relative; width: 9.171em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.302em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.171em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.756em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10497" class="mtd"><span id="MathJax-Span-10498" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10499" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10500" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10501" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10502" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-10503" class="mtd"><span id="MathJax-Span-10504" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10505" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10506" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10507" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10508" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10509" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10511" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10513" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10514" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -0.031em; left: 0em;"><span id="MathJax-Span-10515" class="mtd"><span id="MathJax-Span-10516" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10517" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10518" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10519" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10520" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10521" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10522" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10523" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10524" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10525" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10527" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10528" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10529" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10530" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10531" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10533" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10534" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.919em; vertical-align: -3.001em;"></span></span></nobr></span><script id="MathJax-Element-479" type="math/tex">\begin{array}[t]{l}
-\forall e.~
-\\
-\qquad entity(e)
-\\
-\quad\Rightarrow
-alternateOf(e,e)
-\end{array}</script></div>
-<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-480-Frame" class="MathJax"><nobr><span id="MathJax-Span-10535" class="math"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10536" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10537" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10538" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10540" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10541" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10542" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10543" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10544" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10545" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10546" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-480" type="math/tex">ent = rho(e)</script>. Clearly <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-481-Frame" class="MathJax"><nobr><span id="MathJax-Span-10547" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.772em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10548" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10549" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10550" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10551" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10552" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10554" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10556" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10557" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10558" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-481" type="math/tex">e \in Entities</script> and
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-482-Frame" class="MathJax"><nobr><span id="MathJax-Span-10559" class="math"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10560" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10561" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10562" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10563" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10564" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10565" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10566" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10567" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10568" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10569" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10570" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10571" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10573" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10574" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10575" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10576" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10577" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10578" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10579" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10580" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10581" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-482" type="math/tex">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-483-Frame" class="MathJax"><nobr><span id="MathJax-Span-10582" class="math"><span style="display: inline-block; position: relative; width: 171px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10583" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10584" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10585" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10586" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10587" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10588" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10589" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10590" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10592" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10593" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10596" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10597" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10598" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10599" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10600" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10601" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10602" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10603" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-483" type="math/tex">W,\rho \models alternateOf(e,e)</script>.</p>
- </div>
-<div class="inference" number="17" id="alternate-transitive"><div class="ruleTitle"><a href="#alternate-transitive" class="internalDFN">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-484-Frame" class="MathJax"><nobr><span id="MathJax-Span-10604" class="math"><span style="display: inline-block; position: relative; width: 328px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.06em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10605" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10606" class="mtable"><span style="display: inline-block; position: relative; width: 18.808em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.513em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.808em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10607" class="mtd"><span id="MathJax-Span-10608" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10609" class="mi">∀</span><span id="MathJax-Span-10610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10611" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10613" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10614" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10615" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10616" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10617" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10618" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10619" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10620" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10621" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10622" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-10623" class="mtd"><span id="MathJax-Span-10624" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10625" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10626" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10627" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10628" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10631" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10632" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10633" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10634" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10635" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10636" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10637" class="mo">(</span><span id="MathJax-Span-10638" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10639" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10640" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10641" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10642" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10643" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10644" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10645" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-10646" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-10647" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10651" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10652" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10653" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10655" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10656" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10657" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10658" class="mo">(</span><span id="MathJax-Span-10659" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10660" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10661" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10662" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10663" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10664" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10665" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10666" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.063em; left: 0em;"><span id="MathJax-Span-10667" class="mtd"><span id="MathJax-Span-10668" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10669" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10670" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10672" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10674" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10675" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10676" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10677" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10678" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10679" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10680" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10681" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10682" class="mo">(</span><span id="MathJax-Span-10683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10684" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10686" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10687" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10688" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10689" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10690" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.02em; vertical-align: -3.101em;"></span></span></nobr></span><script id="MathJax-Element-484" type="math/tex">\begin{array}[t]{l}
-\forall e_1,e_2,e_3.~
-\\
-\qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
-\\
-\quad\Rightarrow
-alternateOf(e_1,e_3)
-\end{array}</script></div>
-<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-485-Frame" class="MathJax"><nobr><span id="MathJax-Span-10691" class="math"><span style="display: inline-block; position: relative; width: 101px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10692" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10693" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10694" class="mi">n</span><span id="MathJax-Span-10695" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10697" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10698" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10699" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10700" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10701" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10702" class="mo">(</span><span id="MathJax-Span-10703" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10704" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10705" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10706" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-485" type="math/tex">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-486-Frame" class="MathJax"><nobr><span id="MathJax-Span-10707" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10708" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10709" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10710" class="mi">n</span><span id="MathJax-Span-10711" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10713" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10714" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10715" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10716" class="mo">(</span><span id="MathJax-Span-10717" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10718" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10719" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10720" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-486" type="math/tex">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-487-Frame" class="MathJax"><nobr><span id="MathJax-Span-10721" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10722" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10723" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10724" class="mi">n</span><span id="MathJax-Span-10725" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10726" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10727" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10728" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10729" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10730" class="mo">(</span><span id="MathJax-Span-10731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10733" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10734" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-487" type="math/tex">ent_3 = \rho(e_3)</script>. Then by
- assumption <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-488-Frame" class="MathJax"><nobr><span id="MathJax-Span-10735" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10737" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10738" class="mi">n</span><span id="MathJax-Span-10739" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10740" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10741" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-488" type="math/tex">ent_1</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-489-Frame" class="MathJax"><nobr><span id="MathJax-Span-10742" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10743" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10744" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10745" class="mi">n</span><span id="MathJax-Span-10746" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10747" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10748" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-489" type="math/tex">ent_2</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-490-Frame" class="MathJax"><nobr><span id="MathJax-Span-10749" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10750" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10751" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10752" class="mi">n</span><span id="MathJax-Span-10753" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10754" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10755" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.88em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-490" type="math/tex">ent_3</script> are in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-491-Frame" class="MathJax"><nobr><span id="MathJax-Span-10756" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.758em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10757" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10758" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10759" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10762" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10764" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10765" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.839em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-491" type="math/tex">Entities</script> and
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-492-Frame" class="MathJax"><nobr><span id="MathJax-Span-10766" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10767" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10769" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10771" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10772" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10773" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10774" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10775" class="mo">(</span><span id="MathJax-Span-10776" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10777" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10778" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10779" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10780" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10782" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10783" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10784" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10785" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10786" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10787" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10788" class="mo">(</span><span id="MathJax-Span-10789" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10790" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10791" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10792" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-492" type="math/tex">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-493-Frame" class="MathJax"><nobr><span id="MathJax-Span-10793" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10794" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10796" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10797" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10798" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10799" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10800" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10801" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10802" class="mo">(</span><span id="MathJax-Span-10803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10804" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10805" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10806" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10807" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10809" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10810" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10811" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10812" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10813" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10814" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10815" class="mo">(</span><span id="MathJax-Span-10816" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10817" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10818" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10819" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-493" type="math/tex">thingOf(e_2) = thingOf(e_3)</script>, so
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-494-Frame" class="MathJax"><nobr><span id="MathJax-Span-10820" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10821" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10822" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10823" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10824" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10825" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10826" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10827" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10828" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10829" class="mo">(</span><span id="MathJax-Span-10830" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10831" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10832" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10833" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10834" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10836" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10837" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10838" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10839" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10840" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10841" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10842" class="mo">(</span><span id="MathJax-Span-10843" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10844" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10845" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10846" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-494" type="math/tex">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-495-Frame" class="MathJax"><nobr><span id="MathJax-Span-10847" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10848" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10849" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10851" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10852" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10853" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10854" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10856" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10857" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10858" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10861" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10862" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10863" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10864" class="mo">(</span><span id="MathJax-Span-10865" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10866" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10867" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10868" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10869" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10870" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10871" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10872" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-495" type="math/tex">W,\rho
- \models alternateOf(e_2,e_1)</script>.</p>
- </div>
-<div class="inference" number="18" id="alternate-symmetric"><div class="ruleTitle"><a href="#alternate-symmetric" class="internalDFN">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-496-Frame" class="MathJax"><nobr><span id="MathJax-Span-10873" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10874" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10875" class="mtable"><span style="display: inline-block; position: relative; width: 10.047em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.047em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10876" class="mtd"><span id="MathJax-Span-10877" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10878" class="mi">∀</span><span id="MathJax-Span-10879" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10880" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10881" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10882" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10883" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10884" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10885" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10886" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10887" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-10888" class="mtd"><span id="MathJax-Span-10889" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10890" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10891" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10892" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10895" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10896" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10897" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10898" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10899" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10900" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10901" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10902" class="mo">(</span><span id="MathJax-Span-10903" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10904" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10905" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10906" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10907" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10908" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10909" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10910" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-10911" class="mtd"><span id="MathJax-Span-10912" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10913" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10914" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10916" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10917" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10918" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10919" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10920" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10921" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10922" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10923" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10924" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10925" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10926" class="mo">(</span><span id="MathJax-Span-10927" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10928" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10929" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10930" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10931" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10932" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10933" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10934" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-496" type="math/tex">\begin{array}[t]{l}
-\forall e_1,e_2.~
-\\
-\qquad alternateOf(e_1,e_2)
-\\
-\quad\Rightarrow
-alternateOf(e_2,e_1)
-\end{array}</script></div>
-<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-497-Frame" class="MathJax"><nobr><span id="MathJax-Span-10935" class="math"><span style="display: inline-block; position: relative; width: 101px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10936" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10938" class="mi">n</span><span id="MathJax-Span-10939" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10941" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10942" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10943" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10944" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10945" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10946" class="mo">(</span><span id="MathJax-Span-10947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10948" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10950" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-497" type="math/tex">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-498-Frame" class="MathJax"><nobr><span id="MathJax-Span-10951" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10952" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10953" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10954" class="mi">n</span><span id="MathJax-Span-10955" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10957" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10958" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10959" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10960" class="mo">(</span><span id="MathJax-Span-10961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10962" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10963" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10964" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-498" type="math/tex">ent_2 = \rho(e_2)</script>. Then by
- assumption both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-499-Frame" class="MathJax"><nobr><span id="MathJax-Span-10965" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10966" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10967" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10968" class="mi">n</span><span id="MathJax-Span-10969" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10971" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-499" type="math/tex">ent_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-500-Frame" class="MathJax"><nobr><span id="MathJax-Span-10972" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10973" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10974" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10975" class="mi">n</span><span id="MathJax-Span-10976" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10977" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10978" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-500" type="math/tex">ent_2</script> are in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-501-Frame" class="MathJax"><nobr><span id="MathJax-Span-10979" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.758em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10980" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10981" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10982" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10984" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10985" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10986" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10987" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10988" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.839em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-501" type="math/tex">Entities</script> and
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-502-Frame" class="MathJax"><nobr><span id="MathJax-Span-10989" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10990" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10992" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10995" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10996" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10997" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10998" class="mo">(</span><span id="MathJax-Span-10999" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11000" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11001" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11002" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11003" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11004" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11005" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11006" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11007" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11008" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11009" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11010" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11011" class="mo">(</span><span id="MathJax-Span-11012" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11013" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11014" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11015" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-502" type="math/tex">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-503-Frame" class="MathJax"><nobr><span id="MathJax-Span-11016" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11017" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11018" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11019" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11020" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11021" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11023" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11025" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11026" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11027" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11028" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11029" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11030" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11031" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11032" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11033" class="mo">(</span><span id="MathJax-Span-11034" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11035" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11036" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11037" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11038" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11039" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11040" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11041" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-503" type="math/tex">W,\rho
- \models alternateOf(e_2,e_1)</script>.</p>
- </div>
-
-<div class="inference" number="19" id="specialization-transitive"><div class="ruleTitle"><a href="#specialization-transitive" class="internalDFN">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-504-Frame" class="MathJax"><nobr><span id="MathJax-Span-11042" class="math"><span style="display: inline-block; position: relative; width: 393px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.06em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11043" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11044" class="mtable"><span style="display: inline-block; position: relative; width: 22.605em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.513em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 22.605em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11045" class="mtd"><span id="MathJax-Span-11046" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11047" class="mi">∀</span><span id="MathJax-Span-11048" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11049" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11050" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11054" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11058" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11059" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11060" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-11061" class="mtd"><span id="MathJax-Span-11062" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11063" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11064" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11065" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11066" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11067" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11068" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11069" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11070" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11072" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11073" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11074" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11075" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11076" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11077" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11078" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11079" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11080" class="mo">(</span><span id="MathJax-Span-11081" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11082" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11083" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11086" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11088" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-11089" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-11090" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11091" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11092" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11093" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11094" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11095" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11096" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11097" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11098" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11099" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11100" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11102" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11103" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11104" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11105" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11106" class="mo">(</span><span id="MathJax-Span-11107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11109" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11110" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11111" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11112" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11113" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11114" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.063em; left: 0em;"><span id="MathJax-Span-11115" class="mtd"><span id="MathJax-Span-11116" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11117" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11118" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11119" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11120" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11121" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11122" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11123" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11124" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11125" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11126" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11127" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11128" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11130" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11131" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11132" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11133" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11134" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11135" class="mo">(</span><span id="MathJax-Span-11136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11137" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11139" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11140" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11141" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11142" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11143" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.02em; vertical-align: -3.101em;"></span></span></nobr></span><script id="MathJax-Element-504" type="math/tex">\begin{array}[t]{l}
-\forall e_1,e_2,e_3.~
-\\
-\qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
-\\
-\quad\Rightarrow
-specializationOf(e_1,e_3)
-\end{array}</script></div>
-<div class="proof">
- <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-505-Frame" class="MathJax"><nobr><span id="MathJax-Span-11144" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11145" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11146" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11147" class="mi">n</span><span id="MathJax-Span-11148" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11150" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-505" type="math/tex">ent_1</script> and
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-506-Frame" class="MathJax"><nobr><span id="MathJax-Span-11151" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11152" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11154" class="mi">n</span><span id="MathJax-Span-11155" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11156" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11157" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-506" type="math/tex">ent_2</script> and for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-507-Frame" class="MathJax"><nobr><span id="MathJax-Span-11158" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11159" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11160" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11161" class="mi">n</span><span id="MathJax-Span-11162" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11163" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11164" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-507" type="math/tex">ent_2</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-508-Frame" class="MathJax"><nobr><span id="MathJax-Span-11165" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11166" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11167" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11168" class="mi">n</span><span id="MathJax-Span-11169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11171" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.88em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-508" type="math/tex">ent_3</script>, where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-509-Frame" class="MathJax"><nobr><span id="MathJax-Span-11172" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11173" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11174" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11175" class="mi">n</span><span id="MathJax-Span-11176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11177" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11178" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11179" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11180" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11181" class="mo">(</span><span id="MathJax-Span-11182" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11183" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11184" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11185" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-509" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-510-Frame" class="MathJax"><nobr><span id="MathJax-Span-11186" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11187" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11188" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11189" class="mi">n</span><span id="MathJax-Span-11190" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11191" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11192" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11193" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11194" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11195" class="mo">(</span><span id="MathJax-Span-11196" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11197" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11198" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11199" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-510" type="math/tex">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-511-Frame" class="MathJax"><nobr><span id="MathJax-Span-11200" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11201" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11203" class="mi">n</span><span id="MathJax-Span-11204" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11205" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11206" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11207" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11208" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11209" class="mo">(</span><span id="MathJax-Span-11210" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11211" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11212" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11213" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-511" type="math/tex">ent_3 =
- \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-512-Frame" class="MathJax"><nobr><span id="MathJax-Span-11214" class="math"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11215" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11216" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11217" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11218" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11219" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11220" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11221" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11222" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11223" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11224" class="mo">(</span><span id="MathJax-Span-11225" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11226" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11227" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11228" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11229" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11230" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11232" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11233" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11236" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11237" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11238" class="mo">(</span><span id="MathJax-Span-11239" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11240" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11241" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11242" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11243" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11246" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11250" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11251" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11252" class="mo">(</span><span id="MathJax-Span-11253" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11254" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11255" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11256" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-512" type="math/tex">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
- lifetime(e_3)</script>. Moreover,
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-513-Frame" class="MathJax"><nobr><span id="MathJax-Span-11257" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.998em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11258" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11259" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11261" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11262" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11263" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11264" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11265" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11266" class="mi">b</span><span id="MathJax-Span-11267" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11268" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11269" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11270" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11272" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11274" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11275" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11276" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11277" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11279" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11280" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11281" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11282" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11283" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11284" class="mi">b</span><span id="MathJax-Span-11285" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11286" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11287" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11288" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11289" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11290" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11292" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11293" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.126em; vertical-align: -0.332em;"></span></span></nobr></span><script id="MathJax-Element-513" type="math/tex">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-514-Frame" class="MathJax"><nobr><span id="MathJax-Span-11294" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11295" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11296" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11297" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11298" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11299" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11300" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11301" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11303" class="mi">b</span><span id="MathJax-Span-11304" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11305" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11306" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11307" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11310" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11312" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11313" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11314" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11315" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11316" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11317" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11318" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11319" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11320" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11321" class="mi">b</span><span id="MathJax-Span-11322" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11323" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11324" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11325" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11326" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11327" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11328" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11329" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11330" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-514" type="math/tex">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-515-Frame" class="MathJax"><nobr><span id="MathJax-Span-11331" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.998em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11332" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11333" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11335" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11336" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11337" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11338" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11339" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11340" class="mi">b</span><span id="MathJax-Span-11341" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11342" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11343" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11344" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11348" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11349" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11350" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11351" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11354" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11355" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11356" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11357" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11358" class="mi">b</span><span id="MathJax-Span-11359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11360" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11361" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11362" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11366" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11367" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.126em; vertical-align: -0.332em;"></span></span></nobr></span><script id="MathJax-Element-515" type="math/tex">value(obj_1,attr)
- \supseteq value(obj_3,attr)</script>. (TODO:
- How do we know <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-516-Frame" class="MathJax"><nobr><span id="MathJax-Span-11368" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11369" class="mrow"><span id="MathJax-Span-11370" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11371" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11372" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11373" class="mo">≠</span><span style="padding-left: 0.313em;" id="MathJax-Span-11374" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11375" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11376" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.004em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-516" type="math/tex">e_3 \neq e_1</script>? Need strict ordering on entities in semantics.)
-</p>
-</div>
-
-<div class="inference" number="20" id="specialization-alternate-inference"><div class="ruleTitle"><a href="#specialization-alternate-inference" class="internalDFN">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-517-Frame" class="MathJax"><nobr><span id="MathJax-Span-11377" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11378" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11379" class="mtable"><span style="display: inline-block; position: relative; width: 11.857em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 11.857em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11380" class="mtd"><span id="MathJax-Span-11381" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11382" class="mi">∀</span><span id="MathJax-Span-11383" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11384" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11385" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11386" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11387" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11388" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11389" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11390" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11391" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-11392" class="mtd"><span id="MathJax-Span-11393" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11394" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11395" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11396" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11397" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11398" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11399" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11400" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11401" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11402" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11403" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11404" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11405" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11406" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11407" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11408" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11409" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11410" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11411" class="mo">(</span><span id="MathJax-Span-11412" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11413" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11414" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11415" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11416" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11417" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11418" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11419" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-11420" class="mtd"><span id="MathJax-Span-11421" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11422" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11423" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11425" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11427" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11428" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11429" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11430" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11432" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11433" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11434" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11435" class="mo">(</span><span id="MathJax-Span-11436" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11437" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11438" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11439" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11440" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11441" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11442" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11443" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-517" type="math/tex">\begin{array}[t]{l}
-\forall e_1,e_2.~
-\\
-\qquad specializationOf(e_1,e_2)
-\\
-\quad\Rightarrow
-alternateOf(e_1,e_2)
-\end{array}</script></div>
-<div class="proof">
- <p> If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-518-Frame" class="MathJax"><nobr><span id="MathJax-Span-11444" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11445" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11446" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11447" class="mi">n</span><span id="MathJax-Span-11448" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11450" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11451" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11452" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11453" class="mo">(</span><span id="MathJax-Span-11454" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11455" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11456" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11457" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-518" type="math/tex">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-519-Frame" class="MathJax"><nobr><span id="MathJax-Span-11458" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11459" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11460" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11461" class="mi">n</span><span id="MathJax-Span-11462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11463" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11465" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11466" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11467" class="mo">(</span><span id="MathJax-Span-11468" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11469" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11470" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11471" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-519" type="math/tex">ent_2 = \rho(e_2)</script> are
- specializations, then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-520-Frame" class="MathJax"><nobr><span id="MathJax-Span-11472" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11473" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11475" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11476" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11477" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11478" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11479" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11480" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11481" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11483" class="mi">n</span><span id="MathJax-Span-11484" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11485" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11486" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11487" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11488" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11490" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11492" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11493" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11494" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11495" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11496" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11497" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11498" class="mi">n</span><span id="MathJax-Span-11499" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11500" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11501" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11502" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-520" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>.
-</p>
-</div>
-
-<div class="inference" number="21" id="specialization-attributes-inference"><div class="ruleTitle"><a href="#specialization-attributes-inference" class="internalDFN">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-521-Frame" class="MathJax"><nobr><span id="MathJax-Span-11503" class="math"><span style="display: inline-block; position: relative; width: 334px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11504" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11505" class="mtable"><span style="display: inline-block; position: relative; width: 19.159em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.495em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.159em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11506" class="mtd"><span id="MathJax-Span-11507" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11508" class="mi">∀</span><span id="MathJax-Span-11509" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11510" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11511" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11512" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11513" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11514" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11515" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11516" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11517" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11518" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11519" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11520" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11521" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11522" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11523" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-11524" class="mtd"><span id="MathJax-Span-11525" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11526" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11527" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11528" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11529" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11530" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11532" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11533" class="mo">(</span><span id="MathJax-Span-11534" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11535" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11536" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11537" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11538" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11541" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11542" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11543" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-11544" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-11545" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11546" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11547" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11548" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11549" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11550" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11551" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11552" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11553" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11554" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11556" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11557" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11558" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11559" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11560" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11561" class="mo">(</span><span id="MathJax-Span-11562" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11563" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11564" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11565" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11566" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11567" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11568" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11569" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: 0.046em; left: 0em;"><span id="MathJax-Span-11570" class="mtd"><span id="MathJax-Span-11571" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11572" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11573" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11574" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11575" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11577" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11579" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11580" class="mo">(</span><span id="MathJax-Span-11581" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11582" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11583" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11584" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11585" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11586" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11587" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11588" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11589" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11590" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-521" type="math/tex">\begin{array}[t]{l}
-\forall e_1,attrs,e_2.~
-\\
-\qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
-\\
-\quad\Rightarrow
-entity(e_2,attrs)
-\end{array}</script></div>
-</section>
-<div class="proof">
- <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-522-Frame" class="MathJax"><nobr><span id="MathJax-Span-11591" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11592" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11593" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11594" class="mi">n</span><span id="MathJax-Span-11595" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11597" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11598" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11599" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11600" class="mo">(</span><span id="MathJax-Span-11601" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11602" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11603" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11604" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-522" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-523-Frame" class="MathJax"><nobr><span id="MathJax-Span-11605" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11606" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11607" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11608" class="mi">n</span><span id="MathJax-Span-11609" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11610" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11611" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11612" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11613" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11614" class="mo">(</span><span id="MathJax-Span-11615" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11616" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11617" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11618" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-523" type="math/tex">ent_2 = \rho(e_2)</script>. Suppose
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-524-Frame" class="MathJax"><nobr><span id="MathJax-Span-11619" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11620" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11621" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11622" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11623" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11624" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11625" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11626" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11627" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-524" type="math/tex">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-525-Frame" class="MathJax"><nobr><span id="MathJax-Span-11628" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11629" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11630" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11633" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11634" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-525" type="math/tex">attrs</script>. Since
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-526-Frame" class="MathJax"><nobr><span id="MathJax-Span-11635" class="math"><span style="display: inline-block; position: relative; width: 105px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11636" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11637" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11638" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11639" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11640" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11641" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11642" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11643" class="mo">(</span><span id="MathJax-Span-11644" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11645" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11646" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11647" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11648" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11650" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11651" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11652" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11653" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-526" type="math/tex">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-527-Frame" class="MathJax"><nobr><span id="MathJax-Span-11654" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11655" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11656" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11657" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11658" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11660" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11662" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11663" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11664" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11665" class="mi">n</span><span id="MathJax-Span-11666" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11668" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11669" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11670" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11672" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11673" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-527" type="math/tex">v \in value(ent_1,att)</script>.
- Thus <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-528-Frame" class="MathJax"><nobr><span id="MathJax-Span-11674" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11675" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11676" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11677" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11678" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11680" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11681" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11682" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11683" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11684" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11685" class="mi">n</span><span id="MathJax-Span-11686" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11687" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11688" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11689" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11690" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11691" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11693" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-528" type="math/tex">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-529-Frame" class="MathJax"><nobr><span id="MathJax-Span-11694" class="math"><span style="display: inline-block; position: relative; width: 228px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11695" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11696" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11698" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11699" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11700" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11701" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11702" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11703" class="mi">n</span><span id="MathJax-Span-11704" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11705" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11706" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11707" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11708" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11709" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11711" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11712" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11713" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11714" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11715" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11716" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11717" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11718" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11719" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11720" class="mi">n</span><span id="MathJax-Span-11721" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11722" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11723" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11724" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11725" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11726" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11727" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11728" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-529" type="math/tex">value(ent_2,att) \supseteq value(ent_1,att)</script>. Since
- this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-530-Frame" class="MathJax"><nobr><span id="MathJax-Span-11729" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11730" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11731" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11732" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11733" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11734" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11735" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-530" type="math/tex">attrs</script>, and since
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-531-Frame" class="MathJax"><nobr><span id="MathJax-Span-11736" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11737" class="mrow"><span id="MathJax-Span-11738" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11739" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11740" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-531" type="math/tex">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-532-Frame" class="MathJax"><nobr><span id="MathJax-Span-11741" class="math"><span style="display: inline-block; position: relative; width: 146px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11742" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11743" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11744" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11745" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11746" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11747" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11748" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11750" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11751" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11752" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11753" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11754" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11755" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11756" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11757" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11758" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11759" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11760" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-532" type="math/tex">W,\rho \models entity(e,attrs</script>).
- </p>
-</div>
-
-<section id="constraints">
-<h3><span class="secno">5.2 </span>Constraints</h3>
-<section id="uniqueness-constraints">
-<h4><span class="secno">5.2.1 </span>Uniqueness constraints</h4>
-
-<div class="constraint" number="22" id="key-object"><div class="ruleTitle"><a href="#key-object" class="internalDFN">Constraint 22 (key-object)</a></div>
- <ol><li>The
- identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-533-Frame" class="MathJax"><nobr><span id="MathJax-Span-11761" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11762" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11764" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-533" type="math/tex">id</script> is a <span class="conditional">KEY</span> for
- the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-534-Frame" class="MathJax"><nobr><span id="MathJax-Span-11765" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11766" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11767" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11768" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11772" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11773" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11774" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11775" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11776" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11777" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11778" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11780" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11781" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11782" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-534" type="math/tex">entity(id,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-535-Frame" class="MathJax"><nobr><span id="MathJax-Span-11783" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11784" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11785" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11786" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-535" type="math/tex">id</script>
- is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-536-Frame" class="MathJax"><nobr><span id="MathJax-Span-11787" class="math"><span style="display: inline-block; position: relative; width: 155px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11788" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11789" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11790" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11792" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11793" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11794" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11796" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11797" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11798" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11799" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11800" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11801" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11803" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11804" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11805" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11807" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11808" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11809" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11811" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11812" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11813" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11814" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-536" type="math/tex">activity(id,t_1,t_2,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-537-Frame" class="MathJax"><nobr><span id="MathJax-Span-11815" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11816" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11818" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-537" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-538-Frame" class="MathJax"><nobr><span id="MathJax-Span-11819" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11820" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11822" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11823" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11826" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11827" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11828" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11829" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11830" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11832" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11833" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11834" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11835" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-538" type="math/tex">agent(id,attrs)</script> statement.</li></ol></div>
-<div class="constraint" number="23" id="key-properties"><div class="ruleTitle"><a href="#key-properties" class="internalDFN">Constraint 23 (key-properties)</a></div>
- <ol><li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-539-Frame" class="MathJax"><nobr><span id="MathJax-Span-11836" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11837" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11838" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11839" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-539" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-540-Frame" class="MathJax"><nobr><span id="MathJax-Span-11840" class="math"><span style="display: inline-block; position: relative; width: 227px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11841" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11842" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11843" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11844" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11845" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11846" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11847" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11848" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11849" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11850" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11852" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11853" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11854" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11855" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11856" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11857" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11858" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11859" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11860" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11861" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11862" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11863" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11864" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11865" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11866" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11867" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11869" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11870" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11871" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-540" type="math/tex">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-541-Frame" class="MathJax"><nobr><span id="MathJax-Span-11872" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11873" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11875" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-541" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-542-Frame" class="MathJax"><nobr><span id="MathJax-Span-11876" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11877" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11878" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11879" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11880" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11881" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11882" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11883" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11884" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11886" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11887" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11888" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11889" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11890" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11891" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11892" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11894" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11895" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11896" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11897" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-542" type="math/tex">used(id,a,e,t,attrs)</script>
- statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-543-Frame" class="MathJax"><nobr><span id="MathJax-Span-11898" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11899" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11900" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11901" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-543" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-544-Frame" class="MathJax"><nobr><span id="MathJax-Span-11902" class="math"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11904" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11905" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11906" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11907" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11908" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11909" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11910" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11911" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11912" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11913" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11914" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11915" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11916" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11917" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11918" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11919" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11920" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11921" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11922" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11923" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11924" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11925" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11926" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11927" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11928" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11929" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11930" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11931" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11933" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11934" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-544" type="math/tex">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-545-Frame" class="MathJax"><nobr><span id="MathJax-Span-11935" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11936" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11937" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11938" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-545" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-546-Frame" class="MathJax"><nobr><span id="MathJax-Span-11939" class="math"><span style="display: inline-block; position: relative; width: 236px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11940" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11941" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11942" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11943" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11944" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11945" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11946" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11947" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11949" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11950" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11951" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11952" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11953" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11954" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11955" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11956" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11957" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11958" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11959" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11961" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11962" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11964" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11966" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11967" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11968" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11972" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11973" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11974" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-546" type="math/tex">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-547-Frame" class="MathJax"><nobr><span id="MathJax-Span-11975" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11976" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11978" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-547" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-548-Frame" class="MathJax"><nobr><span id="MathJax-Span-11979" class="math"><span style="display: inline-block; position: relative; width: 230px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11980" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11981" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11983" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11984" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11985" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11986" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11987" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11988" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11989" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11990" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11991" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11992" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11993" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11994" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11995" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11996" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11997" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11998" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11999" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12000" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12002" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12003" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12004" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12007" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12010" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12011" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12012" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-548" type="math/tex">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-549-Frame" class="MathJax"><nobr><span id="MathJax-Span-12013" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12014" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12016" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-549" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-550-Frame" class="MathJax"><nobr><span id="MathJax-Span-12017" class="math"><span style="display: inline-block; position: relative; width: 233px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12018" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12019" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12021" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12022" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12023" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12024" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12025" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12026" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12027" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12028" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12029" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12030" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12031" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12032" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12033" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12034" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12035" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12036" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12037" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12038" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12039" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12040" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12041" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12043" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12044" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12045" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12046" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12047" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12048" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12049" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12050" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-550" type="math/tex">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-551-Frame" class="MathJax"><nobr><span id="MathJax-Span-12051" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12052" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12053" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12054" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-551" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-552-Frame" class="MathJax"><nobr><span id="MathJax-Span-12055" class="math"><span style="display: inline-block; position: relative; width: 295px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12056" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12057" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12058" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12059" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12060" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12061" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12064" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12066" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12067" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12068" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12069" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12070" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12071" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12072" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12073" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12074" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12075" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12076" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12077" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12078" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12080" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12081" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12083" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12086" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12088" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12090" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12091" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12092" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12093" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12094" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12096" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12097" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12098" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-552" type="math/tex">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-553-Frame" class="MathJax"><nobr><span id="MathJax-Span-12099" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12100" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12102" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-553" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-554-Frame" class="MathJax"><nobr><span id="MathJax-Span-12103" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12104" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12105" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12107" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12108" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12109" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12111" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12112" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12113" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12114" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12116" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12117" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12118" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12119" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12120" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12122" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12123" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12124" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12126" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12127" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12128" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12129" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12130" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12131" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12132" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12133" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12134" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-554" type="math/tex">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-555-Frame" class="MathJax"><nobr><span id="MathJax-Span-12135" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12136" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12137" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12138" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-555" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-556-Frame" class="MathJax"><nobr><span id="MathJax-Span-12139" class="math"><span style="display: inline-block; position: relative; width: 262px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12141" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12142" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12143" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12144" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12145" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12146" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12147" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12148" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12149" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12150" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12152" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12153" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12154" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12155" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12156" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12157" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12158" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12159" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12160" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12161" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12162" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12163" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12164" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12165" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12166" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12167" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12168" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12169" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12173" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12174" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12175" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-556" type="math/tex">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-557-Frame" class="MathJax"><nobr><span id="MathJax-Span-12176" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12177" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12178" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12179" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-557" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-558-Frame" class="MathJax"><nobr><span id="MathJax-Span-12180" class="math"><span style="display: inline-block; position: relative; width: 272px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12181" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12183" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12184" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12185" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12186" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12187" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12188" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12189" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12190" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12191" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12192" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12193" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12194" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12195" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12196" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12197" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12198" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12199" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12200" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12201" class="mi">a</span><span id="MathJax-Span-12202" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12203" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12204" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12205" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12206" class="mi">a</span><span id="MathJax-Span-12207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12208" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12209" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12211" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12212" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12213" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12215" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12216" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12217" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12218" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-558" type="math/tex">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
- <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-559-Frame" class="MathJax"><nobr><span id="MathJax-Span-12219" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12220" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12221" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12222" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-559" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-560-Frame" class="MathJax"><nobr><span id="MathJax-Span-12223" class="math"><span style="display: inline-block; position: relative; width: 235px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12224" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12225" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12226" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12227" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12228" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12229" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12230" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12231" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12232" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12233" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12234" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12235" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12237" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12238" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12239" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12240" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12241" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12243" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12244" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12245" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12247" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12248" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12249" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12250" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12251" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12252" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12253" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12254" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12255" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-560" type="math/tex">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
- </div>
-<div class="constraint" number="24" id="unique-generation"><div class="ruleTitle"><a href="#unique-generation" class="internalDFN">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-561-Frame" class="MathJax"><nobr><span id="MathJax-Span-12256" class="math"><span style="display: inline-block; position: relative; width: 582px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.972em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12257" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12258" class="mtable"><span style="display: inline-block; position: relative; width: 33.645em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.366em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.645em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12259" class="mtd"><span id="MathJax-Span-12260" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12261" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12262" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12263" class="mi">e</span><span id="MathJax-Span-12264" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12265" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12266" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12268" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12269" class="mi">e</span><span id="MathJax-Span-12270" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12271" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12272" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12273" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12274" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12276" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12277" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12280" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12281" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12284" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12285" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12288" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12289" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12290" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12291" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12292" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12297" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12298" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12299" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12300" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12301" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12302" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-12303" class="mtd"><span id="MathJax-Span-12304" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12305" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12306" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12307" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12308" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12309" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12311" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12312" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12313" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12316" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12318" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12319" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12321" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12322" class="mi">e</span><span id="MathJax-Span-12323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12324" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12326" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12327" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12328" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12329" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12330" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12331" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12332" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12333" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12334" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12338" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12339" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12340" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12341" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12342" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12343" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12344" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12346" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12347" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12348" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12349" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12350" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12351" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12353" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12354" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12355" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12356" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12357" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12358" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12359" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12360" class="mi">e</span><span id="MathJax-Span-12361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12362" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12363" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12364" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12365" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12367" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12368" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12369" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12371" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12378" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12380" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.951em, -0.526em); top: -0.024em; left: 0em;"><span id="MathJax-Span-12381" class="mtd"><span id="MathJax-Span-12382" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12383" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12384" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12385" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12386" class="mi">e</span><span id="MathJax-Span-12387" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12388" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12389" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12390" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12391" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12392" class="mi">e</span><span id="MathJax-Span-12393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12394" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12395" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.926em; vertical-align: -3.007em;"></span></span></nobr></span><script id="MathJax-Element-561" type="math/tex">\begin{array}[t]{l}
-\forall gen_1,gen_2,e,a,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen_1,e,a,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 = gen_2
-\end{array}</script></div>
-<div class="constraint" number="25" id="unique-invalidation"><div class="ruleTitle"><a href="#unique-invalidation" class="internalDFN">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-562-Frame" class="MathJax"><nobr><span id="MathJax-Span-12396" class="math"><span style="display: inline-block; position: relative; width: 588px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12397" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12398" class="mtable"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.299em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12399" class="mtd"><span id="MathJax-Span-12400" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12401" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12402" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12403" class="mi">n</span><span id="MathJax-Span-12404" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12405" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12406" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12407" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12408" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12409" class="mi">n</span><span id="MathJax-Span-12410" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12411" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12412" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12413" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12414" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12415" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12416" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12417" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12418" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12419" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12420" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12421" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12422" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12424" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12425" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12426" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12429" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12430" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12431" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12432" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12433" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12434" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12435" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12437" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12438" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12439" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12440" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12441" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12442" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-12443" class="mtd"><span id="MathJax-Span-12444" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12445" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12446" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12447" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12448" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12449" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12450" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12451" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12452" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12453" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12454" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12455" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12456" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12457" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12458" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12459" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12460" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12461" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12462" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12463" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12464" class="mi">n</span><span id="MathJax-Span-12465" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12466" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12467" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12468" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12469" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12470" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12471" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12472" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12473" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12475" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12476" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12477" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12478" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12480" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12481" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12482" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12483" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12484" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12485" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12486" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12487" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12488" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12489" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12490" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12491" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12492" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12493" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12494" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12495" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12496" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12497" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12498" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12499" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12500" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12501" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12502" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12504" class="mi">n</span><span id="MathJax-Span-12505" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12506" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12507" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12508" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12509" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12511" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12512" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12513" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12514" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12515" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12516" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12517" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12518" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12519" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12520" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12522" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12523" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12524" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-12525" class="mtd"><span id="MathJax-Span-12526" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12527" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12528" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12529" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12530" class="mi">n</span><span id="MathJax-Span-12531" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12532" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12533" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12534" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12535" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12536" class="mi">n</span><span id="MathJax-Span-12537" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12538" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12539" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-562" type="math/tex">\begin{array}[t]{l}
-\forall inv_1,inv_2,e,a,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasInvalidatedBy(inv_1,e,a,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a,t_2,attrs_2)
-\\
-\quad\Rightarrow
-inv_1 = inv_2
-\end{array}</script></div>
-<div class="constraint" number="26" id="unique-wasStartedBy"><div class="ruleTitle"><a href="#unique-wasStartedBy" class="internalDFN">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-563-Frame" class="MathJax"><nobr><span id="MathJax-Span-12540" class="math"><span style="display: inline-block; position: relative; width: 615px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.92em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12541" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12542" class="mtable"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.148em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12543" class="mtd"><span id="MathJax-Span-12544" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12545" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12546" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12548" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12549" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12550" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12551" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12552" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12553" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12554" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12557" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12558" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12559" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12560" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12561" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12562" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12563" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12564" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12565" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12566" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12567" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12568" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12569" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12570" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12574" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12578" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12579" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12580" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12582" class="mn">2</span><span style="display: inline-block; width: 0px; 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top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12628" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12629" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12630" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12632" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12633" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12634" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12635" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12637" class="mn">1</span><span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12658" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12659" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12660" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12661" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12663" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12664" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12665" class="msubsup"><span style="display: inline-block; 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width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12693" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12694" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12695" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12698" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12699" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12700" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12701" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12702" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12703" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12704" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12705" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12706" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12707" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12709" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.87em; vertical-align: -2.951em;"></span></span></nobr></span><script id="MathJax-Element-563" type="math/tex">\begin{array}[t]{l}
-\forall start_1,start_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start_1,a,e_1,a_0,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_0,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 = start_2
-\end{array}</script></div>
-<div class="constraint" number="27" id="unique-wasEndedBy"><div class="ruleTitle"><a href="#unique-wasEndedBy" class="internalDFN">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-564-Frame" class="MathJax"><nobr><span id="MathJax-Span-12710" class="math"><span style="display: inline-block; position: relative; width: 589px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.052em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12711" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12712" class="mtable"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.396em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12713" class="mtd"><span id="MathJax-Span-12714" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12715" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12717" class="mi">n</span><span id="MathJax-Span-12718" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12719" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12720" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12721" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12722" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12723" class="mi">n</span><span id="MathJax-Span-12724" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12725" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12726" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12727" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12728" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12729" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12730" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12731" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12732" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12733" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12734" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12735" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12736" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12737" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12738" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12739" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12740" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12741" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12742" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12743" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12744" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12745" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12746" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12747" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12748" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12749" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12750" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12751" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12753" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12754" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12755" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12756" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12757" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12758" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12759" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12761" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12762" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12763" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12764" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12765" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12766" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-12767" class="mtd"><span id="MathJax-Span-12768" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12769" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12770" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12771" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12772" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12773" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12774" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12775" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12776" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12777" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12778" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12779" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12780" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12781" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12782" class="mi">n</span><span id="MathJax-Span-12783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12784" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12785" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12786" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12787" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12788" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12789" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12790" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12791" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12792" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12793" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12794" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12795" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12796" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12797" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12798" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12800" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12801" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12803" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12804" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12805" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12806" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12807" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12808" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12809" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12810" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12811" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12812" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12813" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12814" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12815" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12816" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12817" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12818" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12819" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12820" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12822" class="mi">n</span><span id="MathJax-Span-12823" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12824" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12825" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12826" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12827" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12828" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12829" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12830" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12831" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12832" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12833" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12834" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12835" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12836" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12837" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12838" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12839" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12840" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12841" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12842" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12844" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12845" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12846" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12847" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12848" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.062em; left: 0em;"><span id="MathJax-Span-12849" class="mtd"><span id="MathJax-Span-12850" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12851" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12852" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12854" class="mi">n</span><span id="MathJax-Span-12855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12856" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12857" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12858" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12859" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12860" class="mi">n</span><span id="MathJax-Span-12861" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12862" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12863" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.011em; vertical-align: -3.093em;"></span></span></nobr></span><script id="MathJax-Element-564" type="math/tex">\begin{array}[t]{l}
-\forall end_1,end_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasEndedBy(end_1,a,e_1,a_0,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_0,t_2,attrs_2)
-\\
-\quad\Rightarrow
-end_1 = end_2
-\end{array}</script></div>
-<div class="constraint" number="28" id="unique-startTime"><div class="ruleTitle"><a href="#unique-startTime" class="internalDFN">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-565-Frame" class="MathJax"><nobr><span id="MathJax-Span-12864" class="math"><span style="display: inline-block; position: relative; width: 483px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.91em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12865" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12866" class="mtable"><span style="display: inline-block; position: relative; width: 27.862em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.138em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.862em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12867" class="mtd"><span id="MathJax-Span-12868" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12869" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12870" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12871" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12872" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12873" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12874" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12875" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12876" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12877" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12878" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12879" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12880" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12881" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12882" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12883" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12885" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12886" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12887" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12888" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12889" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12890" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12891" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12892" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12893" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12894" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12895" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12896" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12897" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12898" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12899" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12900" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12901" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12902" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12905" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12906" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12907" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12908" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12909" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12910" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-12911" class="mtd"><span id="MathJax-Span-12912" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12913" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12914" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12915" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12917" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12918" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12919" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12920" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12921" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12922" class="mo">(</span><span id="MathJax-Span-12923" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12924" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12925" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12926" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12927" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12928" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12929" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12930" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12931" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12932" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12933" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12934" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12935" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12936" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12939" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12940" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12941" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12942" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12943" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12944" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12945" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12946" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12947" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12948" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12949" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12951" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12952" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12953" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12954" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12955" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12957" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12958" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12959" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12960" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12962" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12963" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12964" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12965" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12966" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12967" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12968" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12969" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12970" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12972" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12973" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12974" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12975" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12976" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12977" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12978" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12979" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12980" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.895em, -0.526em); top: -0.08em; left: 0em;"><span id="MathJax-Span-12981" class="mtd"><span id="MathJax-Span-12982" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12983" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12984" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-12985" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12986" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12987" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12988" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12989" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.859em; vertical-align: -2.941em;"></span></span></nobr></span><script id="MathJax-Element-565" type="math/tex">\begin{array}[t]{l}
-\forall start,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
-\\
-\qquad activity(a_2,t_1,t_2,attrs) \wedge wasStartedBy(start,a_2,e,a_1,t,attrs_1)
-\\
-\quad\Rightarrow
-t_1 = t
-\end{array}</script></div>
-<div class="constraint" number="29" id="unique-endTime"><div class="ruleTitle"><a href="#unique-endTime" class="internalDFN">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-566-Frame" class="MathJax"><nobr><span id="MathJax-Span-12990" class="math"><span style="display: inline-block; position: relative; width: 470px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.91em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12991" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12992" class="mtable"><span style="display: inline-block; position: relative; width: 27.103em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.138em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.103em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12993" class="mtd"><span id="MathJax-Span-12994" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12995" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12996" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12997" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12998" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12999" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13000" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13001" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13002" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13003" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13004" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13005" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13006" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13007" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13009" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13010" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13011" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13012" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13013" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13014" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13016" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13017" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13018" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13019" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13021" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13022" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13023" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13024" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13025" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13026" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13027" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13029" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13030" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13031" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13032" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13033" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13034" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13035" class="mtd"><span id="MathJax-Span-13036" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13037" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13038" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13039" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13042" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13045" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13046" class="mo">(</span><span id="MathJax-Span-13047" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13048" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13049" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13050" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13051" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13053" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13054" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13056" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13057" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13058" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13059" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13063" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13064" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13065" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13066" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13067" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13068" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13069" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13070" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13071" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13073" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13074" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13075" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13076" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13077" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13078" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13079" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13080" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13081" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13082" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13083" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13084" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13085" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13086" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13087" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13088" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13089" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13090" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13091" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13092" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13093" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13094" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13096" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13097" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13098" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13099" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13100" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.895em, -0.526em); top: -0.08em; left: 0em;"><span id="MathJax-Span-13101" class="mtd"><span id="MathJax-Span-13102" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13103" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13104" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-13105" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13106" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13107" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13108" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13109" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.859em; vertical-align: -2.941em;"></span></span></nobr></span><script id="MathJax-Element-566" type="math/tex">\begin{array}[t]{l}
-\forall end,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
-\\
-\qquad activity(a_2,t_1,t_2,attrs) \wedge wasEndedBy(end,a_2,e,a_1,t,attrs_1)
-\\
-\quad\Rightarrow
-t_2 = t
-\end{array}</script></div>
-</section>
-
-<section id="ordering-constraints">
-<h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
-
-
-<div class="constraint" number="30" id="start-precedes-end"><div class="ruleTitle"><a href="#start-precedes-end" class="internalDFN">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-567-Frame" class="MathJax"><nobr><span id="MathJax-Span-13110" class="math"><span style="display: inline-block; position: relative; width: 588px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13111" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13112" class="mtable"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13113" class="mtd"><span id="MathJax-Span-13114" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13115" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13116" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13117" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13118" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13119" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13121" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13123" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13124" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13126" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13127" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13128" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13129" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13130" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13131" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13132" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13133" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13134" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13135" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13137" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13139" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13140" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13141" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13142" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13143" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13144" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13145" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13146" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13147" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13148" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13150" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13151" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13152" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13153" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13154" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13155" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13157" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13158" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13159" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13160" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13161" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13162" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13163" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13164" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13165" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13166" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13167" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13168" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13169" class="mtd"><span id="MathJax-Span-13170" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13171" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13172" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13174" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13175" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13176" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13177" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13178" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13179" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13180" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13181" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13182" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13183" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13184" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13185" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13186" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13187" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13188" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13189" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13190" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13191" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13192" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13194" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13195" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13196" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13197" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13198" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13199" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13200" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13201" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13202" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13203" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13204" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13208" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13209" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13210" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13211" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13212" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13213" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13214" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13215" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13216" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13217" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13218" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13219" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13220" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13221" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13222" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13223" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13224" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13225" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13226" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13227" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13228" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13229" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13230" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13231" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13232" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13233" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13234" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13235" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13236" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13237" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13238" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13239" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13240" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13241" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13242" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13246" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13247" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13248" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13249" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13250" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13251" class="mtd"><span id="MathJax-Span-13252" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13253" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13254" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13255" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13256" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13257" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13258" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13259" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13260" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13261" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13262" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13263" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-567" type="math/tex">\begin{array}[t]{l}
-\forall start,end,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start \preceq end
-\end{array}</script></div>
-<div class="constraint" number="31" id="start-start-ordering"><div class="ruleTitle"><a href="#start-start-ordering" class="internalDFN">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-568-Frame" class="MathJax"><nobr><span id="MathJax-Span-13264" class="math"><span style="display: inline-block; position: relative; width: 615px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.968em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13265" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13266" class="mtable"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.254em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13267" class="mtd"><span id="MathJax-Span-13268" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13269" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13270" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13272" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13273" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13274" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13275" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13276" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13278" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13280" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13281" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13284" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13285" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13286" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13287" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13288" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13289" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13290" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13291" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13292" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13293" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13294" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13295" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13296" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13297" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13298" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13299" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13300" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13301" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13302" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13303" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13304" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13306" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13307" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13308" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13310" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13311" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13314" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13315" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13316" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13317" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13318" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13319" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13321" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13323" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13324" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13325" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13326" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13327" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13328" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13329" class="mtd"><span id="MathJax-Span-13330" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13331" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13332" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13334" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13335" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13337" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13338" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13339" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13340" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13341" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13342" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13343" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13345" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13347" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13348" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13349" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13350" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13351" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13353" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13354" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13355" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13356" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13357" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13358" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13360" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13361" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13362" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13363" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13365" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13367" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13368" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13369" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13370" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13371" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13372" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13373" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13374" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13375" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13376" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13377" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13378" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13379" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13380" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13381" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13382" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13386" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13387" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13388" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13389" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13391" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13392" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13394" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13395" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13396" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13397" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13398" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13399" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13400" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13401" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13402" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13403" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13404" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13405" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13406" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13407" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13408" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13409" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13410" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13411" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13414" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13415" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13416" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13417" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13418" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.895em, -0.526em); top: -0.022em; left: 0em;"><span id="MathJax-Span-13419" class="mtd"><span id="MathJax-Span-13420" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13421" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13422" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13423" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13424" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13425" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13426" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13427" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13429" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13430" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13431" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13433" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13434" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13437" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.921em; vertical-align: -3.003em;"></span></span></nobr></span><script id="MathJax-Element-568" type="math/tex">\begin{array}[t]{l}
-\forall start_1,start_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq start_2
-\end{array}</script></div>
-<div class="constraint" number="32" id="end-end-ordering"><div class="ruleTitle"><a href="#end-end-ordering" class="internalDFN">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-569-Frame" class="MathJax"><nobr><span id="MathJax-Span-13438" class="math"><span style="display: inline-block; position: relative; width: 589px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13439" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13440" class="mtable"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.386em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13441" class="mtd"><span id="MathJax-Span-13442" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13443" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13444" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13445" class="mi">n</span><span id="MathJax-Span-13446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13447" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13448" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13450" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13451" class="mi">n</span><span id="MathJax-Span-13452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13456" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13459" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13463" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13467" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13468" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13471" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13473" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13474" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13476" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13477" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13480" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13484" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13485" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13486" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13487" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13488" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13489" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13490" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13491" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13492" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13493" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13494" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13495" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13496" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13497" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13498" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13499" class="mtd"><span id="MathJax-Span-13500" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13501" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13502" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13504" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13505" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13506" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13507" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13508" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13509" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13510" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13511" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13513" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13514" class="mi">n</span><span id="MathJax-Span-13515" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13516" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13517" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13518" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13519" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13520" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13522" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13523" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13524" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13525" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13526" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13527" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13528" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13529" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13531" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13533" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13535" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13536" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13537" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13538" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13539" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13540" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13541" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13542" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13544" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13545" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13546" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13547" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13548" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13550" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13551" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13552" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13554" class="mi">n</span><span id="MathJax-Span-13555" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13556" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13557" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13558" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13559" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13560" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13561" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13562" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13563" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13564" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13565" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13566" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13567" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13568" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13569" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13570" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13571" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13572" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13573" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13576" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13577" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13578" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13579" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13580" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13581" class="mtd"><span id="MathJax-Span-13582" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13583" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13584" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13585" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13586" class="mi">n</span><span id="MathJax-Span-13587" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13588" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13589" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13590" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13592" class="mi">n</span><span id="MathJax-Span-13593" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13594" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13595" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-569" type="math/tex">\begin{array}[t]{l}
-\forall end_1,end_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasEndedBy(end_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-end_1 \preceq end_2
-\end{array}</script></div>
-<div class="constraint" number="33" id="usage-within-activity"><div class="ruleTitle"><a href="#usage-within-activity" class="internalDFN">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-570-Frame" class="MathJax"><nobr><span id="MathJax-Span-13596" class="math"><span style="display: inline-block; position: relative; width: 505px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.968em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13597" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13598" class="mtable"><span style="display: inline-block; position: relative; width: 29.147em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.149em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 29.147em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13599" class="mtd"><span id="MathJax-Span-13600" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13601" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13602" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13604" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13605" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13606" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13607" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13608" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13609" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13610" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13611" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13612" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13613" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13614" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13615" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13616" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13617" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13618" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13619" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13620" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13621" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13622" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13623" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13624" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13625" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13626" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13628" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13629" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13630" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13632" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13633" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13634" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13637" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13638" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13639" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13640" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13641" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13642" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13643" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13645" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13646" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13647" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13648" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13649" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13650" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13651" class="mtd"><span id="MathJax-Span-13652" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13653" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13654" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13655" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13656" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13657" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13662" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13663" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13664" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13665" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13666" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13669" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13670" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13672" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13673" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13674" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13675" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13676" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13677" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13678" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13679" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13680" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13681" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13682" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13686" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13687" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13688" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13689" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13690" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13691" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13692" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13693" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13694" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13695" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13696" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13697" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13698" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13699" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13700" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13701" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13702" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13703" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13704" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13705" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13706" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13707" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13708" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13709" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13710" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13711" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13713" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13714" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13715" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13718" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13719" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13720" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13721" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13722" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.848em, -0.526em); top: -0.022em; left: 0em;"><span id="MathJax-Span-13723" class="mtd"><span id="MathJax-Span-13724" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13725" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13726" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13727" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13728" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13729" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13730" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13731" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13732" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13733" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13734" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13735" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.921em; vertical-align: -3.003em;"></span></span></nobr></span><script id="MathJax-Element-570" type="math/tex">\begin{array}[t]{l}
-\forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge used(use,a,e_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start \preceq use
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-571-Frame" class="MathJax"><nobr><span id="MathJax-Span-13736" class="math"><span style="display: inline-block; position: relative; width: 491px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13737" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13738" class="mtable"><span style="display: inline-block; position: relative; width: 28.329em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.329em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13739" class="mtd"><span id="MathJax-Span-13740" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13741" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13742" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13743" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13744" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13745" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13746" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13747" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13748" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13749" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13750" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13751" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13752" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13753" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13754" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13755" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13757" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13758" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13759" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13760" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13761" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13762" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13763" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13764" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13765" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13766" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13767" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13768" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13770" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13771" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13772" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13773" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13774" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13775" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13776" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13777" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13778" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13779" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13780" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13783" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13785" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13786" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13787" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13788" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13789" class="mtd"><span id="MathJax-Span-13790" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13791" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13792" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13793" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13794" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13795" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13796" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13797" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13798" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13799" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13800" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13801" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13802" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13804" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13805" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13806" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13809" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13810" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13811" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13812" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13813" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13814" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13815" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13816" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13817" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13818" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13819" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13820" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13822" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13823" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13825" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13826" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13827" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13828" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13829" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13830" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13831" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13832" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13833" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13834" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13835" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13836" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13837" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13838" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13839" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13840" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13841" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13842" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13843" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13844" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13845" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13846" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13847" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13848" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13849" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13850" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13852" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13853" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13854" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13855" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13856" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13857" class="mtd"><span id="MathJax-Span-13858" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13859" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13860" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13861" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13862" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13863" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13864" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13865" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13866" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13867" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-571" type="math/tex">\begin{array}[t]{l}
-\forall use,end,a,e_1,e_2,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad used(use,a,e_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-use \preceq end
-\end{array}</script></li></ol></div>
-<div class="constraint" number="34" id="generation-within-activity"><div class="ruleTitle"><a href="#generation-within-activity" class="internalDFN">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-572-Frame" class="MathJax"><nobr><span id="MathJax-Span-13868" class="math"><span style="display: inline-block; position: relative; width: 592px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13869" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13870" class="mtable"><span style="display: inline-block; position: relative; width: 34.229em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.229em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13871" class="mtd"><span id="MathJax-Span-13872" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13873" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13874" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13875" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13876" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13877" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13878" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13879" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13880" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13881" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13882" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13883" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13884" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13885" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13886" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13887" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13889" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13890" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13891" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13892" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13893" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13894" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13895" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13896" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13897" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13898" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13899" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13900" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13901" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13902" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13904" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13905" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13906" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13907" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13908" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13909" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13910" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13911" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13912" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13913" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13914" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13915" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13917" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13918" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13919" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13920" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13921" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13922" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-13923" class="mtd"><span id="MathJax-Span-13924" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13925" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13926" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13927" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13928" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13929" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13930" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13931" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13933" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13934" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13935" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13936" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13937" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13938" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13939" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13941" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13942" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13943" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13944" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13945" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13946" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13948" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13950" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13951" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13952" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13953" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13954" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13955" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13957" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13958" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13959" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13960" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13961" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13962" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13964" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13966" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13967" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13968" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13970" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13971" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13973" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13974" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13975" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13976" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13977" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13978" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13979" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13980" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13981" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13982" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13983" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13984" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13985" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13986" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13987" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13988" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13989" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13991" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13992" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13993" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13994" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13995" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13996" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13997" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14000" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14002" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14003" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14004" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14005" class="mtd"><span id="MathJax-Span-14006" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14007" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14008" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14009" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14010" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14011" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14012" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14013" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14014" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14015" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14016" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14017" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-572" type="math/tex">\begin{array}[t]{l}
-\forall start,gen,e_1,e_2,a,a_1,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen,e_2,a,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start \preceq gen
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-573-Frame" class="MathJax"><nobr><span id="MathJax-Span-14018" class="math"><span style="display: inline-block; position: relative; width: 557px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14019" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14020" class="mtable"><span style="display: inline-block; position: relative; width: 32.185em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 32.185em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14021" class="mtd"><span id="MathJax-Span-14022" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14023" class="mi">∀</span><span style="font-family: STIXGeneral; 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position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14041" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14042" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14043" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14045" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14046" class="msubsup"><span style="display: inline-block; 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padding-left: 0.188em;" id="MathJax-Span-14064" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14065" class="mtd"><span id="MathJax-Span-14066" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14067" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14068" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14069" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14070" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14071" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14073" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14075" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14076" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14077" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14078" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14079" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14080" class="mi">B</span><span style="font-family: STIXGeneral; 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font-family: STIXGeneral;" id="MathJax-Span-14127" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14128" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14129" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14130" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14131" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14132" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14133" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14134" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14135" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14136" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-14137" class="mtd"><span id="MathJax-Span-14138" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14139" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14140" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14141" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14142" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14143" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14144" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14145" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14146" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14147" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-573" type="math/tex">\begin{array}[t]{l}
-\forall gen,end,e,e_1,a,a_1,t,t_1,attrs,attrs_1.~
-\\
-\qquad wasGeneratedBy(gen,e,a,t,attrs) \wedge wasEndedBy(end,a,e_1,a_1,t_1,attrs_1)
-\\
-\quad\Rightarrow
-gen \preceq end
-\end{array}</script></li></ol></div>
-<div class="constraint" number="35" id="wasInformedBy-ordering"><div class="ruleTitle"><a href="#wasInformedBy-ordering" class="internalDFN">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-574-Frame" class="MathJax"><nobr><span id="MathJax-Span-14148" class="math"><span style="display: inline-block; position: relative; width: 847px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.354em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14149" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14150" class="mtable"><span style="display: inline-block; position: relative; width: 49.124em; height: 0px;"><span style="position: absolute; clip: rect(3.89em, 1000em, 8.002em, -0.526em); top: -4.79em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.124em; height: 0px;"><span style="position: absolute; clip: rect(1.671em, 1000em, 3.059em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14151" class="mtd"><span id="MathJax-Span-14152" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14153" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14154" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14155" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14156" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14157" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14159" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14160" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14161" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14162" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14163" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14164" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14165" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14166" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14167" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14168" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14169" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14170" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14171" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14172" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14173" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.447em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14174" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14175" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14177" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14178" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14179" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14180" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14181" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14182" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.505em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14183" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14184" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14185" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14186" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14187" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14188" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14189" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14190" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14191" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14192" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14195" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14196" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14197" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14199" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14200" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14201" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14202" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14203" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14204" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14205" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14206" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14207" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14209" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14210" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14211" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14212" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14213" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14214" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14215" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14217" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14218" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14219" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14220" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14221" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14222" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14223" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.671em, 1000em, 3.059em, -0.526em); top: -1.082em; left: 0em;"><span id="MathJax-Span-14224" class="mtd"><span id="MathJax-Span-14225" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14226" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14227" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14228" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14229" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14230" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14231" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14232" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14233" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14234" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14235" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14237" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14238" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14239" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14240" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14241" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14243" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14244" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14245" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14246" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14247" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14248" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14249" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14250" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14251" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14252" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14253" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14255" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14256" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14257" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14258" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14259" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14261" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14262" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14264" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14265" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14267" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14268" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14269" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14270" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14271" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14272" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14274" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14275" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14276" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14277" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14279" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14280" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14281" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14283" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14284" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14285" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14286" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14287" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14288" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.447em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14289" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14290" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14291" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14292" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14293" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14294" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14295" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14297" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14298" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14299" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14300" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14301" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14302" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14303" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14304" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14305" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14306" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14307" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14308" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14309" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14311" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14312" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14313" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14314" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14315" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14316" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14318" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14319" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14320" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14321" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14322" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14324" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14325" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14326" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14327" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14328" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14329" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.505em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14330" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14331" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14332" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14333" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14334" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14335" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14336" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14338" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14339" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14340" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14341" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14342" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14343" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.364em; left: 0em;"><span id="MathJax-Span-14344" class="mtd"><span id="MathJax-Span-14345" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14346" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14347" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14348" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14350" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14351" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14352" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14353" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14354" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14355" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14356" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.79em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.335em; vertical-align: -3.416em;"></span></span></nobr></span><script id="MathJax-Element-574" type="math/tex">\begin{array}[t]{l}
-\forall id,start,end,a_1,a_1',a_2,a_2',e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
-\\
-\qquad wasInformedBy(id,a_2,a_1,attrs) \wedge wasStartedBy(start,a_1,e_1,a_1',t_1,attrs_1) \wedge wasEndedBy(end,a_2,e_2,a_2',t_2,attrs_2)
-\\
-\quad\Rightarrow
-start \preceq end
-\end{array}</script></div>
-<div class="constraint" number="36" id="generation-precedes-invalidation"><div class="ruleTitle"><a href="#generation-precedes-invalidation" class="internalDFN">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-575-Frame" class="MathJax"><nobr><span id="MathJax-Span-14357" class="math"><span style="display: inline-block; position: relative; width: 585px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.075em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14358" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14359" class="mtable"><span style="display: inline-block; position: relative; width: 33.82em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.528em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.82em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14360" class="mtd"><span id="MathJax-Span-14361" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14362" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14363" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14364" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14365" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14367" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14368" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14369" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14370" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14371" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14372" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14373" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14374" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14375" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14376" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14378" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14380" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14381" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14382" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14383" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14384" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14385" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14386" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14387" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14388" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14389" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14392" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14394" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14395" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14396" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14397" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14398" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14400" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14401" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14402" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14403" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14404" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14405" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14406" class="mtd"><span id="MathJax-Span-14407" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14408" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14409" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14410" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14411" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14412" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14413" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14414" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14415" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14416" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14417" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14418" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14419" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14420" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14421" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14422" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14423" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14424" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14425" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14426" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14427" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14428" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14429" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14430" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14431" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14432" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14433" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14434" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14435" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14436" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14437" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14439" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14441" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14442" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14443" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14444" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14445" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14446" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14447" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14449" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14450" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14451" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14452" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14453" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14454" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14455" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14456" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14457" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14458" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14459" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14460" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14461" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14462" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14463" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14465" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14466" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14467" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14468" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14471" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14473" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14474" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14476" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14477" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14478" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14480" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14481" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14482" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14483" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14484" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14485" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.526em); top: 0.079em; left: 0em;"><span id="MathJax-Span-14486" class="mtd"><span id="MathJax-Span-14487" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14488" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14489" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14490" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14491" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14492" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14493" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14494" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14495" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14496" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.036em; vertical-align: -3.117em;"></span></span></nobr></span><script id="MathJax-Element-575" type="math/tex">\begin{array}[t]{l}
-\forall gen,inv,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen \preceq inv
-\end{array}</script></div>
-<div class="constraint" number="37" id="generation-precedes-usage"><div class="ruleTitle"><a href="#generation-precedes-usage" class="internalDFN">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-576-Frame" class="MathJax"><nobr><span id="MathJax-Span-14497" class="math"><span style="display: inline-block; position: relative; width: 495px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14498" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14499" class="mtable"><span style="display: inline-block; position: relative; width: 28.563em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.563em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14500" class="mtd"><span id="MathJax-Span-14501" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14502" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14503" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14504" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14505" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14506" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14507" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14508" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14509" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14511" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14512" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14513" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14514" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14515" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14516" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14517" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14518" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14519" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14520" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14522" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14523" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14524" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14525" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14527" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14528" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14529" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14532" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14533" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14534" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14535" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14537" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14538" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14540" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14541" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14542" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14543" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14544" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14545" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14546" class="mtd"><span id="MathJax-Span-14547" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14548" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14549" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14550" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14551" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14552" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14554" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14555" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14556" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14557" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14559" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14560" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14561" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14562" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14563" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14564" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14565" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14566" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14567" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14568" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14569" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14571" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14572" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14573" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14574" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14576" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14577" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14578" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14579" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14581" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14582" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14583" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14584" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14585" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14586" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14587" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14588" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14590" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14591" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14592" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14593" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14594" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14595" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14597" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14598" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14599" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14600" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14601" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14604" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14605" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14606" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14607" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14608" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14609" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14611" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14612" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14613" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14614" class="mtd"><span id="MathJax-Span-14615" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14616" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14617" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14618" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14620" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14621" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14622" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14623" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14624" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-576" type="math/tex">\begin{array}[t]{l}
-\forall gen,use,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen \preceq use
-\end{array}</script></div>
-<div class="constraint" number="38" id="usage-precedes-invalidation"><div class="ruleTitle"><a href="#usage-precedes-invalidation" class="internalDFN">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-577-Frame" class="MathJax"><nobr><span id="MathJax-Span-14625" class="math"><span style="display: inline-block; position: relative; width: 497px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14626" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14627" class="mtable"><span style="display: inline-block; position: relative; width: 28.68em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.252em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.68em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14628" class="mtd"><span id="MathJax-Span-14629" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14630" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14631" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14632" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14633" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14634" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14635" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14636" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14637" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14638" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14639" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14640" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14641" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14642" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14643" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14644" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14645" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14646" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14647" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14648" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14649" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14650" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14651" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14652" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14653" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14655" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14657" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14661" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14662" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14663" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14664" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14665" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14666" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14668" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14669" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14670" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14671" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14672" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14673" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-14674" class="mtd"><span id="MathJax-Span-14675" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14676" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14677" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14678" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14679" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14680" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14681" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14682" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14683" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14684" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14685" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14686" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14687" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14688" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14689" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14690" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14691" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14692" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14693" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14694" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14695" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14696" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14697" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14699" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14700" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14701" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14702" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14703" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14704" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14705" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14706" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14707" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14708" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14709" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14710" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14711" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14712" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14713" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14714" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14715" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14717" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14718" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14719" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14720" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14721" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14722" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14723" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14724" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14725" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14726" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14727" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14728" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14729" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14730" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14731" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14732" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14733" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14734" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14735" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14736" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14737" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14739" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14740" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14741" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14742" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14743" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-14744" class="mtd"><span id="MathJax-Span-14745" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14746" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14747" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14748" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14749" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14750" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14751" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14752" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14753" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14754" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-577" type="math/tex">\begin{array}[t]{l}
-\forall use,inv,a_1,a_2,e,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad used(use,a_1,e,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-use \preceq inv
-\end{array}</script></div>
-<div class="constraint" number="39" id="generation-generation-ordering"><div class="ruleTitle"><a href="#generation-generation-ordering" class="internalDFN">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-578-Frame" class="MathJax"><nobr><span id="MathJax-Span-14755" class="math"><span style="display: inline-block; position: relative; width: 598px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14756" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14757" class="mtable"><span style="display: inline-block; position: relative; width: 34.579em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.579em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14758" class="mtd"><span id="MathJax-Span-14759" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14760" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14761" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14762" class="mi">e</span><span id="MathJax-Span-14763" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14764" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14765" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14766" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14767" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14768" class="mi">e</span><span id="MathJax-Span-14769" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14770" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14771" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14772" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14773" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14774" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14776" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14777" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14778" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14779" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14780" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14781" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14782" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14784" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14785" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14786" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14787" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14789" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14790" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14791" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14792" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14793" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14794" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14795" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14796" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14797" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14798" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14799" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14801" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14802" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14804" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14805" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14806" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14807" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14808" class="mtd"><span id="MathJax-Span-14809" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14810" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14811" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14812" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14813" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14814" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14815" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14816" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14817" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14819" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14820" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14822" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14823" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14824" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14825" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14826" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14827" class="mi">e</span><span id="MathJax-Span-14828" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14829" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14830" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14831" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14832" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14833" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14834" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14835" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14836" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14837" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14838" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14840" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14841" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14842" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14845" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14846" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14847" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14848" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14849" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14850" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14851" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14852" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14853" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14854" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14855" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14856" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14857" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14858" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14861" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14862" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14863" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14864" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14865" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14866" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14867" class="mi">e</span><span id="MathJax-Span-14868" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14869" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14870" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14871" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14872" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14873" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14874" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14875" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14876" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14877" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14878" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14879" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14880" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14881" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14882" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14883" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14885" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14886" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14887" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14888" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14889" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14890" class="mtd"><span id="MathJax-Span-14891" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14892" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14893" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14894" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14895" class="mi">e</span><span id="MathJax-Span-14896" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14897" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14898" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14899" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14900" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14901" class="mi">e</span><span id="MathJax-Span-14902" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14903" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14904" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-578" type="math/tex">\begin{array}[t]{l}
-\forall gen_1,gen_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen_1,e,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \preceq gen_2
-\end{array}</script></div>
-<div class="constraint" number="40" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a href="#invalidation-invalidation-ordering" class="internalDFN">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-579-Frame" class="MathJax"><nobr><span id="MathJax-Span-14905" class="math"><span style="display: inline-block; position: relative; width: 604px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14906" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14907" class="mtable"><span style="display: inline-block; position: relative; width: 34.93em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.299em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.93em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14908" class="mtd"><span id="MathJax-Span-14909" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14910" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14911" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14912" class="mi">n</span><span id="MathJax-Span-14913" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14914" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14915" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14916" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14917" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14918" class="mi">n</span><span id="MathJax-Span-14919" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14920" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14921" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14922" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14923" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14924" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14925" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14926" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14927" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14928" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14929" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14930" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14931" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14932" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14933" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14934" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14935" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14936" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14937" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14939" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14940" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14941" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14942" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14943" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14944" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14946" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14948" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14949" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14950" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14951" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14952" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14953" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14954" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14955" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14956" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14957" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-14958" class="mtd"><span id="MathJax-Span-14959" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14960" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14961" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14962" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14963" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14965" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14966" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14967" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14968" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14969" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14970" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14971" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14972" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14973" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14974" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14975" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14976" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14977" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14978" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14979" class="mi">n</span><span id="MathJax-Span-14980" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14981" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14982" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14983" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14984" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14985" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14986" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14987" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14988" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14989" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14990" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14992" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14993" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14994" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14996" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14997" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14998" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14999" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15000" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15001" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15002" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15003" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15004" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15005" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15006" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15007" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15008" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15009" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15010" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15011" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15012" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15013" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15015" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15016" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15017" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15018" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15019" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15020" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15021" class="mi">n</span><span id="MathJax-Span-15022" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15023" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15024" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15025" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15026" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15029" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15030" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15031" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15032" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15033" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15034" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15035" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15036" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15037" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15039" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15040" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15041" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15042" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15043" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-15044" class="mtd"><span id="MathJax-Span-15045" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15046" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15047" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15048" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15049" class="mi">n</span><span id="MathJax-Span-15050" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15051" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15052" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15053" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15054" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15055" class="mi">n</span><span id="MathJax-Span-15056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15057" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15058" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-579" type="math/tex">\begin{array}[t]{l}
-\forall inv_1,inv_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasInvalidatedBy(inv_1,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-inv_1 \preceq inv_2
-\end{array}</script></div>
-<div class="constraint" number="41" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a href="#derivation-usage-generation-ordering" class="internalDFN">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-580-Frame" class="MathJax"><nobr><span id="MathJax-Span-15059" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15060" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15061" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-580" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-581-Frame" class="MathJax"><nobr><span id="MathJax-Span-15062" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15063" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15064" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15065" class="mi">e</span><span id="MathJax-Span-15066" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15067" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15068" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-581" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-582-Frame" class="MathJax"><nobr><span id="MathJax-Span-15069" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15070" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15071" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15072" class="mi">s</span><span id="MathJax-Span-15073" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15074" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15075" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-582" type="math/tex">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-583-Frame" class="MathJax"><nobr><span id="MathJax-Span-15076" class="math"><span style="display: inline-block; position: relative; width: 686px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15077" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15078" class="mtable"><span style="display: inline-block; position: relative; width: 39.72em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 39.72em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15079" class="mtd"><span id="MathJax-Span-15080" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15081" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15082" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15083" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15084" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15085" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15086" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15087" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15088" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15089" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15090" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15091" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15092" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15093" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15094" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15095" class="mi">e</span><span id="MathJax-Span-15096" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15097" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15098" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15099" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15100" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15101" class="mi">s</span><span id="MathJax-Span-15102" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15103" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15104" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15105" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15108" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15109" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15110" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15111" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15112" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15113" class="mtd"><span id="MathJax-Span-15114" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15115" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15116" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15117" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15118" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15119" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15120" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15121" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15122" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15123" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15124" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15125" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15126" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15127" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15130" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15131" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15132" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15133" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15134" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15135" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15136" class="mi">e</span><span id="MathJax-Span-15137" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15138" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15139" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15140" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15141" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15142" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15143" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15144" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15145" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15146" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15147" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15148" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15149" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15150" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15151" class="mi">s</span><span id="MathJax-Span-15152" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15153" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15154" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15155" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15156" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15157" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15158" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15159" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15160" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15161" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15162" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15164" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15165" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15166" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15167" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15168" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15169" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15170" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15171" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15172" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15173" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15174" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15175" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15176" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15177" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15178" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15179" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15180" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15181" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15182" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15183" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15184" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15185" class="mi">e</span><span id="MathJax-Span-15186" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15187" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15188" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15189" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15190" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15191" class="mi">s</span><span id="MathJax-Span-15192" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15193" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15194" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15195" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15196" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15197" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15199" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15200" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15201" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-15202" class="mtd"><span id="MathJax-Span-15203" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15204" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15205" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15206" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15207" class="mi">s</span><span id="MathJax-Span-15208" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15209" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15210" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15211" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15212" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15213" class="mi">e</span><span id="MathJax-Span-15214" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15215" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15216" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-583" type="math/tex">\begin{array}[t]{l}
-\forall d,e_1,e_2,a,gen_2,use_1,attrs.~
-\\
-\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(d,e_2,e_1,a,gen_2,use_1,attrs)
-\\
-\quad\Rightarrow
-use_1 \preceq gen_2
-\end{array}</script></div>
-<div class="constraint" number="42" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a href="#derivation-generation-generation-ordering" class="internalDFN">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-584-Frame" class="MathJax"><nobr><span id="MathJax-Span-15217" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15218" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15219" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-584" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-585-Frame" class="MathJax"><nobr><span id="MathJax-Span-15220" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15221" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15222" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-585" type="math/tex">g</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-586-Frame" class="MathJax"><nobr><span id="MathJax-Span-15223" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15224" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15225" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-586" type="math/tex">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-587-Frame" class="MathJax"><nobr><span id="MathJax-Span-15226" class="math"><span style="display: inline-block; position: relative; width: 908px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.972em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15227" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15228" class="mtable"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.366em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15229" class="mtd"><span id="MathJax-Span-15230" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15231" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15232" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15233" class="mo">,</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-15348" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15350" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15351" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15352" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15353" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15354" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15355" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15356" class="mi">e</span><span id="MathJax-Span-15357" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15358" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15359" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15362" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15364" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15365" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15366" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15367" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15368" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15369" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15371" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15378" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15379" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15380" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15381" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15382" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15384" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15385" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15387" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15389" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15392" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15393" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15394" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15395" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15396" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15397" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15398" class="mi">e</span><span id="MathJax-Span-15399" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15400" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15401" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15402" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15403" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15404" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15405" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15406" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15407" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15408" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15409" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15410" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15411" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15413" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15414" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15415" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15416" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15417" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15418" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15419" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15420" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15421" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15422" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.951em, -0.526em); top: -0.024em; left: 0em;"><span id="MathJax-Span-15423" class="mtd"><span id="MathJax-Span-15424" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15425" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15426" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15427" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15428" class="mi">e</span><span id="MathJax-Span-15429" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15430" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15431" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15432" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15433" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15434" class="mi">e</span><span id="MathJax-Span-15435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15436" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15437" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.926em; vertical-align: -3.007em;"></span></span></nobr></span><script id="MathJax-Element-587" type="math/tex">\begin{array}[t]{l}
-\forall d,gen_1,gen_2,e_1,e_2,a,a_1,a_2,g,u,t_1,t_2,attrs,attrs_1,attrs_2.~
-\\
-\qquad wasDerivedFrom(d,e_2,e_1,a,g,u,attrs) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \prec gen_2
-\end{array}</script></div>
-<div class="constraint" number="43" id="wasStartedBy-ordering"><div class="ruleTitle"><a href="#wasStartedBy-ordering" class="internalDFN">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-588-Frame" class="MathJax"><nobr><span id="MathJax-Span-15438" class="math"><span style="display: inline-block; position: relative; width: 584px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15439" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15440" class="mtable"><span style="display: inline-block; position: relative; width: 33.762em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.762em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15441" class="mtd"><span id="MathJax-Span-15442" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15443" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15444" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15445" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15446" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15447" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15448" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15450" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15451" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15452" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15453" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15454" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15456" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15459" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15463" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15468" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15473" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15476" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15477" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15479" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15480" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15484" class="mi">t<span style="display: inline-block; 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padding-left: 0.188em;" id="MathJax-Span-15490" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15491" class="mtd"><span id="MathJax-Span-15492" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15493" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15494" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15495" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15496" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15497" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15498" class="mi">e</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-15507" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15508" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15509" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15510" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15511" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15512" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15513" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15514" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15515" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15516" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15517" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15518" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15519" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15520" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15527" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15528" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15529" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15530" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15531" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15532" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15533" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15534" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15535" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15537" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15540" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15541" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15542" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15543" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15544" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15545" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15547" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15548" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15550" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15551" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15552" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15553" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15554" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15555" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15556" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15557" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15558" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15559" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15560" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15561" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15562" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15563" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15565" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15566" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15568" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15569" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15570" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-15571" class="mtd"><span id="MathJax-Span-15572" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15573" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15574" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15575" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15576" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15577" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15578" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15579" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15581" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15582" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-588" type="math/tex">\begin{array}[t]{l}
-\forall gen,start,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasStartedBy(start,a,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen \preceq start
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width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15710" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15711" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15713" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15715" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15716" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15717" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15718" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-15719" class="mtd"><span id="MathJax-Span-15720" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15721" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15722" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15723" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15725" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15726" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15727" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15728" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15729" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15730" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15731" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-589" type="math/tex">\begin{array}[t]{l}
-\forall start,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasStartedBy(start,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start \preceq inv
-\end{array}</script></li></ol></div>
-<div class="constraint" number="44" id="wasEndedBy-ordering"><div class="ruleTitle"><a href="#wasEndedBy-ordering" class="internalDFN">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-590-Frame" class="MathJax"><nobr><span id="MathJax-Span-15732" class="math"><span style="display: inline-block; position: relative; width: 571px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15733" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15734" class="mtable"><span style="display: inline-block; position: relative; width: 33.002em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.002em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15735" class="mtd"><span id="MathJax-Span-15736" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15737" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15738" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15740" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15741" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15742" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15743" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15744" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15745" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15746" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15747" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15748" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15749" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15750" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15751" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15752" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15753" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15754" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15755" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15756" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15757" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15758" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15759" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15760" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15761" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15762" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15763" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15764" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15765" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15766" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15767" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15769" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15770" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15771" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15772" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15773" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15774" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15775" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15776" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15777" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15778" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15779" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15780" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15781" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15782" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15783" class="mtd"><span id="MathJax-Span-15784" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15785" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15786" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15787" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15788" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15789" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15790" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15791" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15792" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15793" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15794" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15796" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15797" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15798" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15799" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15800" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15801" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15802" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15803" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15804" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15805" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15806" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15808" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15809" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15810" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15811" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15812" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15813" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15814" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15815" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15819" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15820" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15821" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15822" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15823" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15824" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15825" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15826" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15827" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15828" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15829" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15830" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15831" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15832" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15833" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15834" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15835" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15836" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15837" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15838" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15839" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15840" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15841" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15842" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15843" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15844" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15845" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15846" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15847" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15848" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15849" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15851" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15853" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15854" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15856" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15857" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15858" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-15859" class="mtd"><span id="MathJax-Span-15860" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15861" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15862" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15863" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15865" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15866" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15867" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15868" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15869" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-590" type="math/tex">\begin{array}[t]{l}
-\forall gen,end,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen \preceq end
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-591-Frame" class="MathJax"><nobr><span id="MathJax-Span-15870" class="math"><span style="display: inline-block; position: relative; width: 573px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15871" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15872" class="mtable"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15873" class="mtd"><span id="MathJax-Span-15874" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15875" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15876" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15877" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15878" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15879" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15880" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15881" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15882" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15883" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15884" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15886" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15887" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15889" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15890" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15891" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15892" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15893" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15894" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15895" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15896" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15897" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15898" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15899" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15900" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15901" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15902" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15903" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15904" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15905" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15906" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15907" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15908" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15909" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15910" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15911" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15912" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15914" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15915" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15916" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15917" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15918" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15919" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15920" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-15921" class="mtd"><span id="MathJax-Span-15922" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15923" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15924" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15925" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15926" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15927" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15928" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15929" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15930" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15931" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15932" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15933" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15934" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15935" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15936" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15937" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15938" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15939" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15940" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15941" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15942" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15943" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15944" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15945" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15946" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15950" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15951" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15954" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15955" class="msubsup"><span style="display: inline-block; 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font-style: italic;" id="MathJax-Span-15962" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15963" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15964" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15965" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15966" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15967" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15968" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15969" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15970" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15978" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15979" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15980" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15981" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15982" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15983" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15984" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15985" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15986" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15987" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15989" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15991" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15993" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15994" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15995" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15996" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15997" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15998" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-15999" class="mtd"><span id="MathJax-Span-16000" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16001" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16002" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16003" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16004" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16005" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16006" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16007" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16008" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16009" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-591" type="math/tex">\begin{array}[t]{l}
-\forall end,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasEndedBy(end,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-end \preceq inv
-\end{array}</script></li></ol></div>
-<div class="constraint" number="45" id="specialization-generation-ordering"><div class="ruleTitle"><a href="#specialization-generation-ordering" class="internalDFN">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-592-Frame" class="MathJax"><nobr><span id="MathJax-Span-16010" class="math"><span style="display: inline-block; position: relative; width: 797px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.031em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16011" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16012" class="mtable"><span style="display: inline-block; position: relative; width: 46.203em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.484em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 46.203em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16013" class="mtd"><span id="MathJax-Span-16014" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16015" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16016" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16017" class="mi">e</span><span id="MathJax-Span-16018" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16019" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16020" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16022" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16023" class="mi">e</span><span id="MathJax-Span-16024" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16025" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16026" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16029" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16030" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16031" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16032" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16033" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16034" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16035" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16036" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16037" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16038" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16039" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16040" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16041" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16042" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16043" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16044" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16046" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16047" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16048" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16049" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16050" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16051" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16052" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16053" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16054" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16055" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16057" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16058" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16059" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16060" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16063" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16064" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16065" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16066" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16067" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-16068" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-16069" class="mtd"><span id="MathJax-Span-16070" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-16071" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16072" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16073" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16075" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16076" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16078" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16079" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16080" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16081" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16082" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16084" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16085" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16086" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16087" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16088" class="mo">(</span><span id="MathJax-Span-16089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16090" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16091" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16092" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16093" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16094" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16095" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16096" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16097" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16098" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16099" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16100" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16101" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16102" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16103" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16104" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16105" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16108" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16109" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16110" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16111" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16112" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16113" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16114" class="mi">e</span><span id="MathJax-Span-16115" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16116" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16117" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16118" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16119" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16120" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16121" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16122" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16123" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16124" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16125" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16126" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16129" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16130" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16131" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16132" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16134" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16135" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16136" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16137" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16138" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16139" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16140" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16141" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16142" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16143" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16145" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16146" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16147" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16148" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16150" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16151" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16152" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16153" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16154" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16155" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16156" class="mi">e</span><span id="MathJax-Span-16157" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16158" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16159" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16160" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16161" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16162" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16163" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16164" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16165" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16166" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16167" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16168" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16171" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16172" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16175" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16176" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16177" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16178" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16179" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16180" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.035em; left: 0em;"><span id="MathJax-Span-16181" class="mtd"><span id="MathJax-Span-16182" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16183" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16184" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16185" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16186" class="mi">e</span><span id="MathJax-Span-16187" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16188" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16189" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16190" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16191" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16192" class="mi">e</span><span id="MathJax-Span-16193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16194" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16195" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.989em; vertical-align: -3.07em;"></span></span></nobr></span><script id="MathJax-Element-592" type="math/tex">\begin{array}[t]{l}
-\forall gen_1,gen_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad specializationOf(e_2,e_1) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \preceq gen_2
-\end{array}</script></div>
-<div class="constraint" number="46" id="specialization-invalidation-ordering"><div class="ruleTitle"><a href="#specialization-invalidation-ordering" class="internalDFN">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-593-Frame" class="MathJax"><nobr><span id="MathJax-Span-16196" class="math"><span style="display: inline-block; position: relative; width: 803px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.014em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16197" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16198" class="mtable"><span style="display: inline-block; position: relative; width: 46.554em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.3em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 46.554em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16199" class="mtd"><span id="MathJax-Span-16200" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16201" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16202" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16203" class="mi">n</span><span id="MathJax-Span-16204" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16205" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16206" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16207" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16208" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16209" class="mi">n</span><span id="MathJax-Span-16210" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16211" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16212" class="mn">2</span><span style="display: inline-block; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16326" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16327" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16328" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16329" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16331" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16332" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16333" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16335" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16338" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16339" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16340" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16341" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16342" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16343" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16345" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16346" class="mi">n</span><span id="MathJax-Span-16347" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16348" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16349" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16350" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16351" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16352" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16353" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16354" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16355" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16356" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16357" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16358" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16360" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16361" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16362" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16366" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16367" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16368" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16369" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16370" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.024em; left: 0em;"><span id="MathJax-Span-16371" class="mtd"><span id="MathJax-Span-16372" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16373" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16374" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16375" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16376" class="mi">n</span><span id="MathJax-Span-16377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16378" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16379" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16380" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16381" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16382" class="mi">n</span><span id="MathJax-Span-16383" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16384" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16385" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.971em; vertical-align: -3.052em;"></span></span></nobr></span><script id="MathJax-Element-593" type="math/tex">\begin{array}[t]{l}
-\forall inv_1,inv_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad specializationOf(e_1,e_2) \wedge wasInvalidatedBy(inv_1,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-inv_1 \preceq inv_2
-\end{array}</script></div>
-<div class="constraint" number="47" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a href="#wasAssociatedWith-ordering" class="internalDFN">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-594-Frame" class="MathJax"><nobr><span id="MathJax-Span-16386" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16387" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16388" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16389" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-594" type="math/tex">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-595-Frame" class="MathJax"><nobr><span id="MathJax-Span-16390" class="math"><span style="display: inline-block; position: relative; width: 925px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.069em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16391" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16392" class="mtable"><span style="display: inline-block; position: relative; width: 53.68em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.413em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.68em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16393" class="mtd"><span id="MathJax-Span-16394" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16395" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16396" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16397" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16398" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16399" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16400" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16401" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16402" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16403" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16404" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16405" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16406" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16407" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16408" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16409" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16410" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16411" class="mi">n</span><span id="MathJax-Span-16412" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16413" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16414" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16415" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16416" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16417" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16418" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16419" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16420" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16421" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16422" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16423" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16424" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16425" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16426" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16427" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16428" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16429" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16430" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16431" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16432" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16433" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16434" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16437" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16438" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16439" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16441" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16442" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16443" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16444" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16445" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16446" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16447" class="msubsup"><span style="display: inline-block; 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padding-left: 0.25em;" id="MathJax-Span-16502" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16504" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16505" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16506" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16507" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16508" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16509" class="mi">t<span style="display: inline-block; 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font-style: italic;" id="MathJax-Span-16570" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16574" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16578" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16579" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16580" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16582" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16583" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16585" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16586" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16587" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.079em; left: 0em;"><span id="MathJax-Span-16588" class="mtd"><span id="MathJax-Span-16589" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16590" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16591" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16592" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16595" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16598" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16599" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16600" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16601" class="mi">n</span><span id="MathJax-Span-16602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16603" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16604" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.029em; vertical-align: -3.111em;"></span></span></nobr></span><script id="MathJax-Element-595" type="math/tex">\begin{array}[t]{l}
-\forall assoc,start_1,inv_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-596-Frame" class="MathJax"><nobr><span id="MathJax-Span-16605" class="math"><span style="display: inline-block; position: relative; width: 908px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16606" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16607" class="mtable"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16608" class="mtd"><span id="MathJax-Span-16609" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16610" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16611" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16612" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16613" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16614" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16615" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16616" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16617" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16618" class="mi">e</span><span id="MathJax-Span-16619" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16620" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16621" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16622" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16623" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16624" class="mi">n</span><span id="MathJax-Span-16625" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16626" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16627" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16628" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16630" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16631" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16632" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16633" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16634" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16635" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16636" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16637" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16638" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16639" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16640" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16641" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16642" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16643" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16644" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16645" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16646" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16647" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16648" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16650" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16651" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16653" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16654" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16656" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16657" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16659" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16660" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16661" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16662" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16663" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16664" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16665" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16666" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16667" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16668" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16669" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16670" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16671" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-16672" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-16673" class="mtd"><span id="MathJax-Span-16674" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-16675" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16676" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16677" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16678" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16679" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16680" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16681" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16682" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16683" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16684" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16685" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16686" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16687" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16688" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16689" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16690" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16691" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16692" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16693" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16694" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16695" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16696" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16697" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16698" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16699" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16700" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16701" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16702" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16703" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16704" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16705" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16706" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16707" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16708" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16709" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16711" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16712" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16713" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16714" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16715" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16716" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16717" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16718" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16719" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16720" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16721" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16722" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16723" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16725" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16726" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16727" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16728" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16729" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16730" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16731" class="mi">e</span><span id="MathJax-Span-16732" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16733" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16734" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16735" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16736" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16737" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16738" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16739" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16740" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16741" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16742" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16743" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16745" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16747" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16748" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16750" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16751" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16752" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16753" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16754" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16755" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16756" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16757" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16758" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16759" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16760" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16761" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16762" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16763" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16764" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16765" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16766" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16767" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16768" class="mi">n</span><span id="MathJax-Span-16769" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16770" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16771" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16772" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16773" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16774" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16776" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16777" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16778" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16779" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16780" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16781" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16782" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16784" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16785" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16786" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16787" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16789" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16790" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16791" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16792" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16793" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16794" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-16795" class="mtd"><span id="MathJax-Span-16796" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16797" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16798" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16799" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16800" class="mi">e</span><span id="MathJax-Span-16801" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16802" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16803" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16804" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16805" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16806" class="mi">n</span><span id="MathJax-Span-16807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16808" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16809" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-596" type="math/tex">\begin{array}[t]{l}
-\forall assoc,gen_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \preceq end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-597-Frame" class="MathJax"><nobr><span id="MathJax-Span-16810" class="math"><span style="display: inline-block; position: relative; width: 916px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16811" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16812" class="mtable"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16813" class="mtd"><span id="MathJax-Span-16814" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16815" class="mi">∀</span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16854" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16856" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16857" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16858" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16859" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16861" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16862" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16863" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16864" class="mi">t<span style="display: inline-block; 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clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16876" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16877" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16878" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-16879" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-16880" class="mtd"><span id="MathJax-Span-16881" class="mrow"><span style="height: 0em; 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font-style: italic;" id="MathJax-Span-16892" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16895" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16896" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16897" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16898" class="mi">t<span style="display: inline-block; overflow: hidden; 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position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16941" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16942" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16943" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16944" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16946" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16948" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16949" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16950" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16951" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16952" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16953" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16954" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16955" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16956" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16957" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16958" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16959" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16960" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16962" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16963" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16964" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16965" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16966" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16967" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16968" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16969" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16970" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16971" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16977" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16978" class="mi">n</span><span id="MathJax-Span-16979" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16980" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16981" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16982" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16983" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16984" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16985" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16986" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16987" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16988" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16989" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16990" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16991" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16992" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16993" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16994" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16996" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16997" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16998" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17000" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17001" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17002" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17003" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17004" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17005" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-17006" class="mtd"><span id="MathJax-Span-17007" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17008" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17009" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17010" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17011" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17012" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17013" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17014" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17016" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17017" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17018" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17019" class="mi">n</span><span id="MathJax-Span-17020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17021" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17022" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-597" type="math/tex">\begin{array}[t]{l}
-\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq end_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-598-Frame" class="MathJax"><nobr><span id="MathJax-Span-17023" class="math"><span style="display: inline-block; position: relative; width: 916px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17024" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17025" class="mtable"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17026" class="mtd"><span id="MathJax-Span-17027" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17028" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17029" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17030" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17032" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17033" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17034" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17035" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17036" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17037" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17038" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17039" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17041" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17043" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17044" class="mi">n</span><span id="MathJax-Span-17045" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17046" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17047" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17048" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17049" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17050" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17054" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17058" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17059" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17060" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17061" class="mi">a</span><span style="display: inline-block; 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position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17176" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17177" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17178" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17179" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17180" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17181" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17182" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17183" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17184" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17185" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17186" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17187" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17188" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17189" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17190" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17192" class="mi">n</span><span id="MathJax-Span-17193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17194" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17195" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17196" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17197" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17198" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17199" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17200" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17201" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17202" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17203" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17204" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17205" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17206" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17209" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17211" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17214" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17215" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17216" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17217" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17218" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-17219" class="mtd"><span id="MathJax-Span-17220" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17221" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17222" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17223" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17224" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17226" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17227" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17229" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17230" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17231" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17232" class="mi">n</span><span id="MathJax-Span-17233" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17234" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17235" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-598" type="math/tex">\begin{array}[t]{l}
-\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
-\\
-\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq end_2
-\end{array}</script></li></ol></div>
-<div class="constraint" number="48" id="wasAttributedTo-ordering"><div class="ruleTitle"><a href="#wasAttributedTo-ordering" class="internalDFN">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-599-Frame" class="MathJax"><nobr><span id="MathJax-Span-17236" class="math"><span style="display: inline-block; position: relative; width: 853px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17237" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17238" class="mtable"><span style="display: inline-block; position: relative; width: 49.474em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.474em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17239" class="mtd"><span id="MathJax-Span-17240" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17241" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17242" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17243" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17245" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17246" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17247" class="mi">e</span><span id="MathJax-Span-17248" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17249" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17250" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17251" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17252" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17253" class="mi">e</span><span id="MathJax-Span-17254" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17255" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17256" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17257" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17258" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17259" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17260" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17261" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17262" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17263" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17264" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17265" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17266" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17267" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17268" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17269" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17270" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17271" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17272" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17274" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17276" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17277" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17278" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17279" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17280" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17281" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17282" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17283" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17284" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17285" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17286" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17288" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17289" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17290" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17291" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17292" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17293" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17294" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17296" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17297" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17298" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17299" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17300" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-17301" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-17302" class="mtd"><span id="MathJax-Span-17303" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-17304" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17305" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17306" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17307" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17308" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17310" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17312" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17313" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17314" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17316" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17318" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17319" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17321" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17324" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17325" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17326" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17327" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17328" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17329" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17330" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17331" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17332" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17333" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17334" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17335" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17336" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17337" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17338" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17339" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17340" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17341" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17342" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17343" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17344" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17347" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17348" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17349" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17350" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17351" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17352" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17353" class="mi">e</span><span id="MathJax-Span-17354" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17355" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17356" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17357" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17358" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17359" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17362" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17364" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17365" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17367" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17368" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17369" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17371" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17372" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17373" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17374" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17375" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17376" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17377" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17378" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17379" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17380" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17381" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17382" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17383" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17385" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17386" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17387" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17389" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17390" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17391" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17392" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17393" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17394" class="mi">e</span><span id="MathJax-Span-17395" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17396" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17397" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17398" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17399" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17400" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17401" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17402" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17403" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17404" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17405" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17406" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17407" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17408" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17409" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17411" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17412" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17413" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17414" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17415" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17416" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-17417" class="mtd"><span id="MathJax-Span-17418" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17419" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17420" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17421" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17422" class="mi">e</span><span id="MathJax-Span-17423" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17424" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17425" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17426" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17427" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17428" class="mi">e</span><span id="MathJax-Span-17429" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17430" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17431" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-599" type="math/tex">\begin{array}[t]{l}
-\forall att,gen_1,gen_2,e,a_1,a_2,t_1,t_2,ag,attrs,attrs_1,attrs_2.~
-\\
-\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \preceq gen_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-600-Frame" class="MathJax"><nobr><span id="MathJax-Span-17432" class="math"><span style="display: inline-block; position: relative; width: 861px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17433" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17434" class="mtable"><span style="display: inline-block; position: relative; width: 49.942em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.942em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17435" class="mtd"><span id="MathJax-Span-17436" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17437" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17439" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17441" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17442" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17443" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17444" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17445" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17447" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17448" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17450" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17451" class="mi">e</span><span id="MathJax-Span-17452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17453" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17456" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17459" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17463" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17464" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17467" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17468" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17469" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17471" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17472" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17473" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17475" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17476" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17477" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17478" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17479" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17481" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17484" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17485" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17486" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17487" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17490" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17491" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17492" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17493" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17494" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17495" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17496" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17497" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17498" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17499" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17500" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17501" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17502" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-17503" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-17504" class="mtd"><span id="MathJax-Span-17505" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-17506" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17507" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17509" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17510" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17511" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17512" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17513" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17514" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17515" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17516" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17517" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17518" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17519" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17520" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17521" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17522" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17523" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17526" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17527" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17528" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17529" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17530" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17531" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17532" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17533" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17535" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17536" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17537" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17538" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17539" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17540" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17541" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17542" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17543" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17544" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17545" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17547" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17548" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17549" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17550" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17551" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17552" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17554" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17555" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17556" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17557" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17558" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17559" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17560" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17561" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17562" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17564" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17565" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17566" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17568" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17569" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17570" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17571" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17573" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17574" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17575" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17578" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17579" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17580" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17581" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17582" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17583" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17584" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17585" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17586" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17587" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17588" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17589" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17591" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17592" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17595" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17596" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17597" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17598" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17600" class="mi">e</span><span id="MathJax-Span-17601" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17602" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17603" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17604" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17605" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17606" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17607" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17608" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17609" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17610" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17611" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17612" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17613" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17614" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17615" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17616" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17618" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17619" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17620" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17621" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17622" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-17623" class="mtd"><span id="MathJax-Span-17624" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17625" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17626" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17627" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17628" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17633" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17634" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17635" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17636" class="mi">e</span><span id="MathJax-Span-17637" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17638" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17639" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-600" type="math/tex">\begin{array}[t]{l}
-\forall att,start_1,gen_2,e,e_1,a_1,a_2,ag,t_1,t_2,attrs,attrs_1,attrs_2.~
-\\
-\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq gen_2
-\end{array}</script></li></ol></div>
-<div class="constraint" number="49" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a href="#actedOnBehalfOf-ordering" class="internalDFN">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-601-Frame" class="MathJax"><nobr><span id="MathJax-Span-17640" class="math"><span style="display: inline-block; position: relative; width: 934px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.145em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17641" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17642" class="mtable"><span style="display: inline-block; position: relative; width: 54.206em; height: 0px;"><span style="position: absolute; clip: rect(3.756em, 1000em, 7.715em, -0.526em); top: -4.614em; left: 0em;"><span style="display: inline-block; position: relative; width: 54.206em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17643" class="mtd"><span id="MathJax-Span-17644" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17645" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17646" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17647" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17649" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17650" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17651" class="mi">e</span><span id="MathJax-Span-17652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17653" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17654" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17656" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17657" class="mi">n</span><span id="MathJax-Span-17658" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17659" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17660" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17661" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17662" class="mi">a</span><span id="MathJax-Span-17663" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17664" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17665" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17666" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17667" class="mi">a</span><span id="MathJax-Span-17668" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17669" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17670" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17671" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17672" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17673" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17674" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17675" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17676" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17677" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17678" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17679" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17680" class="mn">2</span><span style="display: inline-block; 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position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17794" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17795" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17796" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17797" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17798" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17799" class="mi">a</span><span style="font-family: STIXGeneral; 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height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17808" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17809" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17810" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17811" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17812" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17813" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17814" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17815" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17816" class="mi">n</span><span id="MathJax-Span-17817" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17818" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17819" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17820" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17821" class="mi">a</span><span id="MathJax-Span-17822" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17823" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17824" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17825" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17826" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17827" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17828" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17829" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17830" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17832" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17833" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17834" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17837" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17838" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17839" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17840" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17841" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.526em); top: 0.15em; left: 0em;"><span id="MathJax-Span-17842" class="mtd"><span id="MathJax-Span-17843" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17844" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17845" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17846" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17847" class="mi">e</span><span id="MathJax-Span-17848" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17849" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17850" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17851" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17852" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17853" class="mi">n</span><span id="MathJax-Span-17854" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17855" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17856" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.614em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.112em; vertical-align: -3.193em;"></span></span></nobr></span><script id="MathJax-Element-601" type="math/tex">\begin{array}[t]{l}
-\forall del,gen_1,inv_2,ag_1,ag_2,a,a_1,a_2,t_1,t_2,attrs,attrs_1,attrs_2.~
-\\
-\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasGeneratedBy(gen_1,ag_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-gen_1 \preceq inv_2
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-602-Frame" class="MathJax"><nobr><span id="MathJax-Span-17857" class="math"><span style="display: inline-block; position: relative; width: 933px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.168em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17858" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17859" class="mtable"><span style="display: inline-block; position: relative; width: 54.147em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.63em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 54.147em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17860" class="mtd"><span id="MathJax-Span-17861" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17862" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17863" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17865" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17866" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17867" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17869" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17870" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17871" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17872" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17873" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17874" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17875" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17876" class="mi">n</span><span id="MathJax-Span-17877" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17878" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17879" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17880" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17881" class="mi">a</span><span id="MathJax-Span-17882" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17883" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17884" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17886" class="mi">a</span><span id="MathJax-Span-17887" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17888" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17889" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17890" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17891" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17892" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17893" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17894" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17895" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17896" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17897" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17898" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17899" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17900" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17901" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17902" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17903" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17904" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17905" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17906" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17907" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17908" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17909" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17910" class="mi">t<span style="display: inline-block; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18026" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18027" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18028" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18029" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18032" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18033" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18034" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18035" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18036" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18037" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18038" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18039" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18040" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18041" class="mi">n</span><span id="MathJax-Span-18042" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18043" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18044" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18045" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18046" class="mi">a</span><span id="MathJax-Span-18047" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18048" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18049" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18050" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18051" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18052" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18053" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18054" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18056" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18057" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18058" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18059" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18061" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18062" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18063" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18064" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18065" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18066" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-18067" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18068" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18069" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18070" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-18071" class="mtd"><span id="MathJax-Span-18072" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18073" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18074" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18075" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18076" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18078" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-18079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18080" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18081" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-18082" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18083" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18084" class="mi">n</span><span id="MathJax-Span-18085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18086" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.136em; vertical-align: -3.218em;"></span></span></nobr></span><script id="MathJax-Element-602" type="math/tex">\begin{array}[t]{l}
-\forall del,start_1,end_2,ag_1,ag_2,a,a_1,a_2,e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
-\\
-\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasStartedBy(start_1,ag_1,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag_2,e_2,a_2,t_2,attrs_2)
-\\
-\quad\Rightarrow
-start_1 \preceq end_2
-\end{array}</script></li></ol></div>
-
-</section>
-
-<section id="typing-constraints">
-<h4><span class="secno">5.2.3 </span>Typing constraints</h4>
-
-<div class="constraint" number="50" id="typing"><div class="ruleTitle"><a href="#typing" class="internalDFN">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-603-Frame" class="MathJax"><nobr><span id="MathJax-Span-18088" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.028em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18089" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18090" class="mtable"><span style="display: inline-block; position: relative; width: 8.995em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.481em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.995em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18091" class="mtd"><span id="MathJax-Span-18092" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18093" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18094" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18095" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18096" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18097" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18098" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18099" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18100" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18101" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18102" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.303em; left: 0em;"><span id="MathJax-Span-18103" class="mtd"><span id="MathJax-Span-18104" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18105" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18106" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18107" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18108" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18109" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18111" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18112" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18113" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18114" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18115" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18117" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18118" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18119" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18120" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.031em; left: 0em;"><span id="MathJax-Span-18121" class="mtd"><span id="MathJax-Span-18122" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18123" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18124" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18125" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18126" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18127" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18128" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18129" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18130" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18131" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18132" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18133" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18134" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18135" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18136" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18137" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18138" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18139" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18140" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.986em; vertical-align: -3.067em;"></span></span></nobr></span><script id="MathJax-Element-603" type="math/tex">\begin{array}[t]{l}
-\forall e,attrs.~
-\\
-\qquad entity(e,attrs)
-\\
-\quad\Rightarrow
-typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-604-Frame" class="MathJax"><nobr><span id="MathJax-Span-18141" class="math"><span style="display: inline-block; position: relative; width: 169px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.093em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18142" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18143" class="mtable"><span style="display: inline-block; position: relative; width: 9.521em; height: 0px;"><span style="position: absolute; clip: rect(3.719em, 1000em, 7.604em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.521em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18144" class="mtd"><span id="MathJax-Span-18145" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18146" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18147" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18148" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18149" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18150" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18152" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18153" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18154" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18155" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18156" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.238em; left: 0em;"><span id="MathJax-Span-18157" class="mtd"><span id="MathJax-Span-18158" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18159" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18160" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18161" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18162" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18163" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18164" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18165" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18166" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18167" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18168" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18169" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18172" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18173" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18174" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.096em; left: 0em;"><span id="MathJax-Span-18175" class="mtd"><span id="MathJax-Span-18176" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18177" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18178" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18179" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18180" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18181" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18182" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18183" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18184" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18185" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18187" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18188" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18189" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18190" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18192" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18194" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.055em; vertical-align: -3.137em;"></span></span></nobr></span><script id="MathJax-Element-604" type="math/tex">\begin{array}[t]{l}
-\forall ag,attrs.~
-\\
-\qquad agent(ag,attrs)
-\\
-\quad\Rightarrow
-typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-605-Frame" class="MathJax"><nobr><span id="MathJax-Span-18195" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.037em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18196" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18197" class="mtable"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.49em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18198" class="mtd"><span id="MathJax-Span-18199" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18200" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18201" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18202" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18203" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18204" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18205" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18206" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18209" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18211" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18214" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18215" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18216" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18217" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.294em; left: 0em;"><span id="MathJax-Span-18218" class="mtd"><span id="MathJax-Span-18219" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18220" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18221" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18222" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18223" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18224" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18225" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18226" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18228" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18229" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18230" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18231" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18232" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18234" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18235" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18236" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18237" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18238" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18239" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18240" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18241" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18242" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18243" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18244" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18245" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.04em; left: 0em;"><span id="MathJax-Span-18246" class="mtd"><span id="MathJax-Span-18247" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18248" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18249" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18251" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18252" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18253" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18254" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18255" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18256" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18257" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18258" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18259" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18260" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18262" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18263" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18264" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18265" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18266" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18267" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.995em; vertical-align: -3.077em;"></span></span></nobr></span><script id="MathJax-Element-605" type="math/tex">\begin{array}[t]{l}
-\forall a,t_1,t_2,attrs.~
-\\
-\qquad activity(a,t_1,t_2,attrs)
-\\
-\quad\Rightarrow
-typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-606-Frame" class="MathJax"><nobr><span id="MathJax-Span-18268" class="math"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.006em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18269" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18270" class="mtable"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.4em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18271" class="mtd"><span id="MathJax-Span-18272" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18273" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18274" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18276" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18278" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18279" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18280" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18281" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18282" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18284" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18285" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18286" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18287" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18288" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-18289" class="mtd"><span id="MathJax-Span-18290" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18291" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18292" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18293" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18294" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18295" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18296" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18297" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18298" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18299" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18300" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18301" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18302" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18303" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18305" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18306" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18307" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18308" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18309" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18310" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.009em; left: 0em;"><span id="MathJax-Span-18311" class="mtd"><span id="MathJax-Span-18312" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18313" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18314" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18316" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18317" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18318" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18319" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18320" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18321" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18322" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18324" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18325" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18326" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18327" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18328" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18329" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18330" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18331" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18332" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18333" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18335" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18336" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18338" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18339" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18340" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18341" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18342" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18343" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18344" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18345" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18346" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18348" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18349" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.962em; vertical-align: -3.044em;"></span></span></nobr></span><script id="MathJax-Element-606" type="math/tex">\begin{array}[t]{l}
-\forall u,a,e,t,attrs.~
-\\
-\qquad used(u,a,e,t,attrs)
-\\
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font-style: italic;" id="MathJax-Span-18365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18367" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18368" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18369" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18370" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-18371" class="mtd"><span id="MathJax-Span-18372" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18373" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18374" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18375" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18376" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18377" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18378" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18379" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18380" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18381" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18382" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18386" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18387" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18388" class="mo">(</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-18398" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18400" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18401" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18402" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.103em; left: 0em;"><span id="MathJax-Span-18403" class="mtd"><span id="MathJax-Span-18404" class="mrow"><span style="height: 0em; 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font-style: italic;" id="MathJax-Span-18422" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18423" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18424" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18425" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18427" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18428" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18429" class="mi">e</span><span style="font-family: STIXGeneral; 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-\\
-\quad\Rightarrow
-typeOf(a,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-608-Frame" class="MathJax"><nobr><span id="MathJax-Span-18442" class="math"><span style="display: inline-block; position: relative; width: 335px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.102em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18443" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18444" class="mtable"><span style="display: inline-block; position: relative; width: 19.217em; height: 0px;"><span style="position: absolute; clip: rect(3.703em, 1000em, 7.613em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.217em; height: 0px;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18445" class="mtd"><span id="MathJax-Span-18446" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18447" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18448" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18449" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18450" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18451" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18453" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18455" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18456" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18457" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18458" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18459" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18460" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18462" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18463" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18464" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18465" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18466" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18467" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18468" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.23em; left: 0em;"><span id="MathJax-Span-18469" class="mtd"><span id="MathJax-Span-18470" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18471" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18472" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18473" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18474" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18475" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18476" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18477" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18478" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18479" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18480" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18481" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18482" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18483" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18484" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18485" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18486" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18487" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18488" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18489" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18490" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18491" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18492" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18493" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18494" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18495" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18496" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18497" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18498" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18499" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18500" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18501" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18502" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18503" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18504" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18505" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.105em; left: 0em;"><span id="MathJax-Span-18506" class="mtd"><span id="MathJax-Span-18507" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18508" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18509" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18511" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18512" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18513" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18514" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18515" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18516" class="mo">(</span><span id="MathJax-Span-18517" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18518" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18519" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18520" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18521" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18522" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18523" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18524" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18525" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18527" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18528" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18529" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18530" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18532" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18533" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18534" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18535" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18536" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18537" class="mo">(</span><span id="MathJax-Span-18538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18539" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18540" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18541" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18542" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18543" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18546" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18547" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18549" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18550" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.065em; vertical-align: -3.146em;"></span></span></nobr></span><script id="MathJax-Element-608" type="math/tex">\begin{array}[t]{l}
-\forall inf,a_2,a_1,t,attrs.~
-\\
-\qquad wasInformedBy(inf,a_2,a_1,t,attrs)
-\\
-\quad\Rightarrow
-typeOf(a_1,activity) \wedge typeOf(a_2,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-609-Frame" class="MathJax"><nobr><span id="MathJax-Span-18551" class="math"><span style="display: inline-block; position: relative; width: 468px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.044em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18552" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18553" class="mtable"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.497em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18554" class="mtd"><span id="MathJax-Span-18555" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18556" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18557" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18560" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18561" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18562" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18564" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18565" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18566" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18567" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18568" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18569" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18570" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18571" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18572" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18573" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18574" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18575" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18578" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18579" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18580" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18581" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-18582" class="mtd"><span id="MathJax-Span-18583" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18584" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18585" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18586" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18587" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18588" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18589" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18590" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18591" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18592" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18593" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18594" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18595" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18596" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18597" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18598" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18599" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18600" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18601" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18603" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18604" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18605" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18606" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18607" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18608" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18609" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18611" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18613" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18614" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18615" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18616" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18619" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18620" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18621" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.047em; left: 0em;"><span id="MathJax-Span-18622" class="mtd"><span id="MathJax-Span-18623" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18624" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18625" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18626" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18627" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18628" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18630" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18631" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18632" class="mo">(</span><span id="MathJax-Span-18633" class="msubsup"><span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18648" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18649" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18651" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18652" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18653" class="mo">(</span><span id="MathJax-Span-18654" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18655" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18656" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18657" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18658" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18659" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18660" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18661" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18662" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18663" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18664" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18665" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18666" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18667" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18669" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18670" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18671" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18672" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18673" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18674" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18675" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18676" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18677" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18678" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18679" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18680" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18681" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18682" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18683" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.003em; vertical-align: -3.084em;"></span></span></nobr></span><script id="MathJax-Element-609" type="math/tex">\begin{array}[t]{l}
-\forall start,a_2,e,a_1,t,attrs.~
-\\
-\qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
-\\
-\quad\Rightarrow
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font-style: italic;" id="MathJax-Span-18727" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18728" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18729" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18732" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18733" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18735" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18736" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18737" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18738" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18739" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18740" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18741" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18742" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18743" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18746" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18747" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18748" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.047em; left: 0em;"><span id="MathJax-Span-18749" class="mtd"><span id="MathJax-Span-18750" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18751" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18752" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18753" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18762" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18763" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18764" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18765" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18767" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18768" class="mi">v</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-18777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18778" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18779" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18780" class="mo">(</span><span id="MathJax-Span-18781" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18782" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18783" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18785" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18786" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18787" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18788" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18789" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18790" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18792" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18793" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18794" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18796" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18797" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18799" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18800" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18801" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18802" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18803" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18804" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18805" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18807" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18809" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18810" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.003em; vertical-align: -3.084em;"></span></span></nobr></span><script id="MathJax-Element-610" type="math/tex">\begin{array}[t]{l}
-\forall end,a_2,e,a_1,t,attrs.~
-\\
-\qquad wasEndedBy(end,a_2,e,a_1,t,attrs)
-\\
-\quad\Rightarrow
-typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-611-Frame" class="MathJax"><nobr><span id="MathJax-Span-18811" class="math"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.035em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18812" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18813" class="mtable"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.488em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18814" class="mtd"><span id="MathJax-Span-18815" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18816" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18818" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18819" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18820" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18821" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18822" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18823" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18824" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18826" class="mo">,</span><span style="font-family: STIXGeneral; 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width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.993em; vertical-align: -3.075em;"></span></span></nobr></span><script id="MathJax-Element-611" type="math/tex">\begin{array}[t]{l}
-\forall inv,a,e,t,attrs.~
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font-style: italic;" id="MathJax-Span-18999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19000" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19002" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19003" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19004" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19005" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19006" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19007" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19008" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19009" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19010" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19011" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19012" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19013" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19014" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19015" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19016" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19017" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19018" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19019" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19020" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19021" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19022" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19023" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19024" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.174em; left: 0em;"><span id="MathJax-Span-19025" class="mtd"><span id="MathJax-Span-19026" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19027" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19028" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19029" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19038" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19039" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19040" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19041" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19042" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19044" class="mi">t<span style="display: inline-block; 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font-style: italic;" id="MathJax-Span-19053" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19054" class="mo">(</span><span id="MathJax-Span-19055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19056" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19057" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19058" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19059" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19060" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19062" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19063" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19064" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19065" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19066" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19067" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19068" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19069" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19070" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19071" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19073" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19074" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19075" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19076" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19077" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19078" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19079" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19080" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19082" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19085" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19086" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.614em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.138em; vertical-align: -3.22em;"></span></span></nobr></span><script id="MathJax-Element-612" type="math/tex">\begin{array}[t]{l}
-\forall id,e_2,e_1,a,g_2,u_1,attrs.~
-\\
-\qquad notNull(a) \wedge notNull(g_2) \wedge notNull(u_1) \wedge wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)
-\\
-\quad\Rightarrow
-typeOf(e_2,entity) \wedge typeOf(e_1,activity) \wedge typeOf(a,activity)
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height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19135" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19137" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19139" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19140" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19141" class="mo">,</span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.972em; vertical-align: -3.053em;"></span></span></nobr></span><script id="MathJax-Element-613" type="math/tex">\begin{array}[t]{l}
-\forall id,e_2,e_1,attrs.~
-\\
-\qquad wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)
-\\
-\quad\Rightarrow
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-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-614-Frame" class="MathJax"><nobr><span id="MathJax-Span-19195" class="math"><span style="display: inline-block; position: relative; width: 302px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.1em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19196" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19197" class="mtable"><span style="display: inline-block; position: relative; width: 17.29em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.611em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.29em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19198" class="mtd"><span id="MathJax-Span-19199" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19200" class="mi">∀</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-19255" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19256" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19257" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19258" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19259" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19260" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19261" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19262" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19263" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19264" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19265" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19267" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19268" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19269" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19271" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19272" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19273" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19274" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19275" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19276" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19277" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19278" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19279" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19280" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19281" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19282" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19283" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19284" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19285" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.063em; vertical-align: -3.144em;"></span></span></nobr></span><script id="MathJax-Element-614" type="math/tex">\begin{array}[t]{l}
-\forall id,e,ag,attrs.~
-\\
-\qquad wasAttributedTo(id,e,ag,attrs)
-\\
-\quad\Rightarrow
-typeOf(e,entity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-615-Frame" class="MathJax"><nobr><span id="MathJax-Span-19286" class="math"><span style="display: inline-block; position: relative; width: 454px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19287" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19288" class="mtable"><span style="display: inline-block; position: relative; width: 26.168em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 26.168em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19289" class="mtd"><span id="MathJax-Span-19290" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19291" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19292" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19293" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19294" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19295" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19296" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19297" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19298" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19300" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19301" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19302" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19303" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19304" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19306" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19307" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19308" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19309" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-19310" class="mtd"><span id="MathJax-Span-19311" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19312" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19313" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19314" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19316" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19317" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19318" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19319" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19321" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19322" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19323" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19324" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19325" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19326" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19327" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19328" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19329" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19331" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19332" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19333" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19335" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19336" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19338" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19339" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19340" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19341" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19342" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19343" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19344" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19345" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19346" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19347" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19348" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19349" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19350" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19351" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19352" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19353" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19354" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19355" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19356" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19357" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19358" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19359" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-19360" class="mtd"><span id="MathJax-Span-19361" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19362" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19363" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19365" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19366" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19367" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19368" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19369" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19370" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19371" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19374" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19376" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19377" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19378" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19379" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19380" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19381" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19382" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19384" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19385" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19387" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19388" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19389" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19391" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19392" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19394" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19395" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19396" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19397" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19398" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19399" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19400" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19401" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19402" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19403" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19404" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19405" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19406" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19407" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19408" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19409" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19410" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19411" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19413" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19415" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19416" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-615" type="math/tex">\begin{array}[t]{l}
-\forall id,a,ag,pl,attrs.~
-\\
-\qquad notNull(pl) \wedge wasAssociatedWith(id,a,ag,pl,attrs)
-\\
-\quad\Rightarrow
-typeOf(a,activity) \wedge typeOf(ag,agent) \wedge typeOf(pl,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-616-Frame" class="MathJax"><nobr><span id="MathJax-Span-19417" class="math"><span style="display: inline-block; position: relative; width: 315px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.1em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19418" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19419" class="mtable"><span style="display: inline-block; position: relative; width: 18.049em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.611em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.049em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19420" class="mtd"><span id="MathJax-Span-19421" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19422" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19423" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19424" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19425" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19426" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19427" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19428" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19429" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19430" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19431" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19433" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19434" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19435" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19436" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19437" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-19438" class="mtd"><span id="MathJax-Span-19439" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19440" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19441" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19442" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19443" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19444" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19445" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19446" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19447" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19448" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19449" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19450" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19452" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19454" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19455" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19456" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19457" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19458" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19459" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19460" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19462" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19463" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19464" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19465" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19466" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19467" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19468" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19469" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19470" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19472" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19473" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19474" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.103em; left: 0em;"><span id="MathJax-Span-19475" class="mtd"><span id="MathJax-Span-19476" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19477" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19478" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19480" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19481" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19483" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19484" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19485" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19486" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19487" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19489" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19490" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19492" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19493" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19494" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19495" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19496" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19497" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19498" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19499" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19500" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19502" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19503" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19504" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19505" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19506" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19507" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19509" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19510" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19511" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19512" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19513" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.063em; vertical-align: -3.144em;"></span></span></nobr></span><script id="MathJax-Element-616" type="math/tex">\begin{array}[t]{l}
-\forall id,a,ag,attrs.~
-\\
-\qquad wasAssociatedWith(id,a,ag,-,attrs)
-\\
-\quad\Rightarrow
-typeOf(a,activity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-617-Frame" class="MathJax"><nobr><span id="MathJax-Span-19514" class="math"><span style="display: inline-block; position: relative; width: 472px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.205em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19515" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19516" class="mtable"><span style="display: inline-block; position: relative; width: 27.22em; height: 0px;"><span style="position: absolute; clip: rect(3.815em, 1000em, 7.833em, -0.526em); top: -4.673em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.22em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19517" class="mtd"><span id="MathJax-Span-19518" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19519" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19520" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19521" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19522" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19523" class="mi">a</span><span id="MathJax-Span-19524" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19525" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19526" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19527" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19528" class="mi">a</span><span id="MathJax-Span-19529" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19530" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19531" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19533" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19534" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19535" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19539" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19540" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19541" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-19542" class="mtd"><span id="MathJax-Span-19543" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19544" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19545" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19546" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19548" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19550" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19551" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19552" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19554" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19555" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19556" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19557" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19558" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19559" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19560" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19561" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19562" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19563" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19564" class="mi">a</span><span id="MathJax-Span-19565" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19566" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19567" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19568" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19569" class="mi">a</span><span id="MathJax-Span-19570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19571" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19572" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19573" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19574" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19575" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19576" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19579" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19580" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19581" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.987em, -0.526em); top: 0.174em; left: 0em;"><span id="MathJax-Span-19582" class="mtd"><span id="MathJax-Span-19583" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19584" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19585" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19586" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19587" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19588" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19590" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19591" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19592" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19593" class="mi">a</span><span id="MathJax-Span-19594" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19595" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19596" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19597" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19598" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19603" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19604" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19606" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19607" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19608" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19609" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19610" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19611" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19612" class="mi">a</span><span id="MathJax-Span-19613" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19614" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19615" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19616" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19617" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19618" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19620" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19621" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19622" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19623" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19624" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19625" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19626" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19628" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19629" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19630" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19631" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19632" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19633" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19634" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19636" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19637" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19638" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19639" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19640" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19641" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.175em; vertical-align: -3.257em;"></span></span></nobr></span><script id="MathJax-Element-617" type="math/tex">\begin{array}[t]{l}
-\forall id,ag_2,ag_1,a,attrs.~
-\\
-\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
-\\
-\quad\Rightarrow
-typeOf(ag_2,agent) \wedge typeOf(ag_1,agent) \wedge typeOf(a,activity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-618-Frame" class="MathJax"><nobr><span id="MathJax-Span-19642" class="math"><span style="display: inline-block; position: relative; width: 308px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.045em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19643" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19644" class="mtable"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.498em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19645" class="mtd"><span id="MathJax-Span-19646" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19647" class="mi">∀</span><span id="MathJax-Span-19648" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19649" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19650" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19651" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19653" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19654" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19655" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19656" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-19657" class="mtd"><span id="MathJax-Span-19658" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19659" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19661" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19663" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19664" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19665" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19668" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19669" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19670" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19671" class="mo">(</span><span id="MathJax-Span-19672" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19673" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19674" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19675" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19676" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19677" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19678" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19679" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.048em; left: 0em;"><span id="MathJax-Span-19680" class="mtd"><span id="MathJax-Span-19681" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19682" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19683" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19685" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19686" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19687" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19688" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19689" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19690" class="mo">(</span><span id="MathJax-Span-19691" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19692" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19693" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19694" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19695" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19696" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19697" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19698" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19700" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19701" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19702" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19703" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19704" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19705" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19706" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19707" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19708" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19709" class="mo">(</span><span id="MathJax-Span-19710" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19711" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19712" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19713" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19714" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19715" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19717" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19719" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19720" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.004em; vertical-align: -3.085em;"></span></span></nobr></span><script id="MathJax-Element-618" type="math/tex">\begin{array}[t]{l}
-\forall e_2,e_1.~
-\\
-\qquad alternateOf(e_2,e_1)
-\\
-\quad\Rightarrow
-typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-619-Frame" class="MathJax"><nobr><span id="MathJax-Span-19721" class="math"><span style="display: inline-block; position: relative; width: 308px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.045em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19722" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19723" class="mtable"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.498em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19724" class="mtd"><span id="MathJax-Span-19725" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19726" class="mi">∀</span><span id="MathJax-Span-19727" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19728" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19729" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19733" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19734" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19735" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-19736" class="mtd"><span id="MathJax-Span-19737" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19738" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19739" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19740" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19741" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19742" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19743" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19744" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19745" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19746" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19747" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19748" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19750" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19751" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19752" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19753" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19754" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19755" class="mo">(</span><span id="MathJax-Span-19756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19757" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19758" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19759" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19760" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19761" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19762" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19763" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.048em; left: 0em;"><span id="MathJax-Span-19764" class="mtd"><span id="MathJax-Span-19765" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19766" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19767" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19769" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19770" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19771" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19772" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19773" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19774" class="mo">(</span><span id="MathJax-Span-19775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19776" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19777" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19778" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19779" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19780" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19782" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19783" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19784" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19785" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19786" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19787" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19788" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19789" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19790" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19791" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19792" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19793" class="mo">(</span><span id="MathJax-Span-19794" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19795" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19796" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19797" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19799" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19801" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19803" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19804" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.004em; vertical-align: -3.085em;"></span></span></nobr></span><script id="MathJax-Element-619" type="math/tex">\begin{array}[t]{l}
-\forall e_2,e_1.~
-\\
-\qquad specializationOf(e_2,e_1)
-\\
-\quad\Rightarrow
-typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-620-Frame" class="MathJax"><nobr><span id="MathJax-Span-19805" class="math"><span style="display: inline-block; position: relative; width: 374px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.011em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19806" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19807" class="mtable"><span style="display: inline-block; position: relative; width: 21.495em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.405em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 21.495em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19808" class="mtd"><span id="MathJax-Span-19809" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19810" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19811" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19812" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19813" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19814" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19815" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-19816" class="mtd"><span id="MathJax-Span-19817" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19818" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19819" class="mi">h</span><span style="font-family: STIXGeneral; 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height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19829" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19830" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19831" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19832" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.014em; left: 0em;"><span id="MathJax-Span-19833" class="mtd"><span id="MathJax-Span-19834" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19835" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19836" class="mo">⇒</span><span style="font-family: STIXGeneral; 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font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19846" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19847" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19848" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19849" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-19850" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19851" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19852" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19853" class="mi">l<span style="display: inline-block; 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padding-left: 0.25em;" id="MathJax-Span-19862" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19864" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19865" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19866" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19867" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19868" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19869" class="mo">(</span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.967em; vertical-align: -3.049em;"></span></span></nobr></span><script id="MathJax-Element-620" type="math/tex">\begin{array}[t]{l}
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font-style: italic;" id="MathJax-Span-19993" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-19994" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19995" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19996" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19997" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19999" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20000" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20001" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20002" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20003" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20004" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20005" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20006" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20007" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20008" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20009" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20010" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.919em; vertical-align: -3.001em;"></span></span></nobr></span><script id="MathJax-Element-621" type="math/tex">\begin{array}[t]{l}
-\forall c.~
-\\
-\qquad entity(c,[prov:type = prov:emptyCollection]))
-\\
-\quad\Rightarrow
-typeOf(c,entity) \wedge typeOf(c,prov:Collection) \wedge typeOf(c,prov:EmptyCollection)
-\end{array}</script></li></ol></div>
-<div class="proof">
- <p>Each typing constraint follows immediately from well-formedness
- criteria marked [WF] in the corresponding semantics for formulas.
- </p>
- </div>
-</section>
-
-<section id="impossibility-constraints">
-<h4><span class="secno">5.2.4 </span>Impossibility constraints</h4>
-
-<div class="constraint" number="51" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a href="#impossible-unspecified-derivation-generation-use" class="internalDFN">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-622-Frame" class="MathJax"><nobr><span id="MathJax-Span-20011" class="math"><span style="display: inline-block; position: relative; width: 422px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20012" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20013" class="mtable"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.279em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20014" class="mtd"><span id="MathJax-Span-20015" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20016" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20017" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20018" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20019" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20021" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20022" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20023" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20024" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20025" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20026" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20027" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20028" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20029" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20031" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20032" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20033" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20034" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20035" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20036" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-20037" class="mtd"><span id="MathJax-Span-20038" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20039" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20040" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20041" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20042" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20043" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20044" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20045" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20046" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20047" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20048" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20049" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20050" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20051" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20052" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20053" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20054" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20055" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20056" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20057" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20058" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20059" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20060" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20061" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20063" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20064" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20065" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20066" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20067" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20068" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20069" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20070" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20071" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20072" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20073" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20074" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20075" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20076" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20077" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20078" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20079" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20080" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20081" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20083" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20085" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20086" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20087" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20088" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-20089" class="mtd"><span id="MathJax-Span-20090" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20091" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20092" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20093" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20094" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20095" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20096" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20097" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-622" type="math/tex">\begin{array}[t]{l}
-\forall id,e_1,e_2,g,attrs.~
-\\
-\qquad notNull(g) \wedge wasDerivedFrom(id,e_2,e_1,-,g,-,attrs)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-623-Frame" class="MathJax"><nobr><span id="MathJax-Span-20098" class="math"><span style="display: inline-block; position: relative; width: 422px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20099" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20100" class="mtable"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.136em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20101" class="mtd"><span id="MathJax-Span-20102" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20103" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20104" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20105" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20106" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20109" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20110" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20111" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20112" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20113" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20114" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20115" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20116" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20117" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20118" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20119" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20120" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20121" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20122" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20123" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-20124" class="mtd"><span id="MathJax-Span-20125" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20126" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20127" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20130" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; 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position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20157" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20158" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20159" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20160" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20161" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20162" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20163" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20164" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20165" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20166" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20167" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20168" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20169" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20173" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20174" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20175" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); 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height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20259" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20260" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20261" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20262" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20263" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20264" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20265" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20266" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20268" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20269" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20270" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20272" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20273" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20274" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20275" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-20276" class="mtd"><span id="MathJax-Span-20277" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20278" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20279" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20280" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20281" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20282" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20283" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20284" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-624" type="math/tex">\begin{array}[t]{l}
-\forall id,e_1,e_2,g,u,attrs.~
-\\
-\qquad notNull(g) \wedge notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,g,u,attrs)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></li></ol></div>
-<div class="proof">
- <p>Each part follows from the fact that the semantics of
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-625-Frame" class="MathJax"><nobr><span id="MathJax-Span-20285" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20286" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20287" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20288" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20290" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20291" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20292" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20294" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20295" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20296" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20297" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20298" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20299" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20300" class="mi">m</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-625" type="math/tex">wasDerivedFrom</script> only allows formulas to hold when either all three
- of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-626-Frame" class="MathJax"><nobr><span id="MathJax-Span-20301" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20302" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20303" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20305" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20306" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20307" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-626" type="math/tex">a,g,u</script> are <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-627-Frame" class="MathJax"><nobr><span id="MathJax-Span-20308" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20309" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20310" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-627" type="math/tex">-</script> (denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-628-Frame" class="MathJax"><nobr><span id="MathJax-Span-20311" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.745em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20312" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20313" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.833em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-628" type="math/tex">\bot</script>) or none of them are.</p>
- </div>
-<div class="constraint" number="52" id="impossible-specialization-reflexive"><div class="ruleTitle"><a href="#impossible-specialization-reflexive" class="internalDFN">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-629-Frame" class="MathJax"><nobr><span id="MathJax-Span-20314" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.96em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20315" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20316" class="mtable"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(3.427em, 1000em, 7.024em, -0.526em); top: -4.264em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.756em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20317" class="mtd"><span id="MathJax-Span-20318" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20319" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20320" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20321" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20322" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-20323" class="mtd"><span id="MathJax-Span-20324" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20325" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20326" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20327" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20328" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20329" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20330" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20331" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20332" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20333" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20334" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20337" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20338" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20339" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20340" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20341" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20342" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20343" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20344" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20345" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20346" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: -0.03em; left: 0em;"><span id="MathJax-Span-20347" class="mtd"><span id="MathJax-Span-20348" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20349" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20350" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20351" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20354" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20355" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.264em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.913em; vertical-align: -2.994em;"></span></span></nobr></span><script id="MathJax-Element-629" type="math/tex">\begin{array}[t]{l}
-\forall e.~
-\\
-\qquad specializationOf(e,e)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></div>
-<div class="proof">
- <p>This follows from the fact that in the semantics of
- <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-630-Frame" class="MathJax"><nobr><span id="MathJax-Span-20356" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20357" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20358" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20359" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20360" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20361" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20362" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20364" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20365" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20366" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20367" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20368" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20369" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20370" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20371" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20372" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20373" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-630" type="math/tex">specializationOf</script>, the two entities denoted by the first and second
- arguments are required to be distinct.
- </p>
- </div>
-<div class="constraint" number="53" id="impossible-property-overlap"><div class="ruleTitle"><a href="#impossible-property-overlap" class="internalDFN">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-631-Frame" class="MathJax"><nobr><span id="MathJax-Span-20374" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20375" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.597em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-631" type="math/tex">r</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-632-Frame" class="MathJax"><nobr><span id="MathJax-Span-20377" class="math"><span style="display: inline-block; position: relative; width: 1050px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20378" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20379" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20380" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20381" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20382" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20383" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20386" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20387" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20388" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20389" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20390" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20391" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20392" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20393" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20394" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20395" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20397" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20398" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20399" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20400" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20401" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20402" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20403" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20404" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20405" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20406" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20407" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20408" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20409" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20410" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20411" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20412" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20414" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20415" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20416" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20417" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20418" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20419" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20420" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20421" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20422" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20425" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20427" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20428" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20429" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20430" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20431" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20432" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20433" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20434" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20435" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20436" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20437" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20438" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20439" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20440" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20441" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20442" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20443" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20444" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20445" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20446" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20447" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20448" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20449" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20450" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20451" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20452" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20454" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20455" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20456" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20457" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20459" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20460" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20461" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20462" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20463" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20465" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20466" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20468" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20469" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20470" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20471" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20472" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20473" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20475" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20476" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20477" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20478" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20479" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20480" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20481" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20485" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20486" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20487" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20489" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20490" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20491" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20492" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20493" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20494" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20495" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20496" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20497" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20498" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20499" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20500" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20501" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20502" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20503" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20504" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20505" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20506" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-632" type="math/tex">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-633-Frame" class="MathJax"><nobr><span id="MathJax-Span-20507" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20508" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20509" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.597em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-633" type="math/tex">r</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-634-Frame" class="MathJax"><nobr><span id="MathJax-Span-20510" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20511" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20512" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-634" type="math/tex">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-635-Frame" class="MathJax"><nobr><span id="MathJax-Span-20513" class="math"><span style="display: inline-block; position: relative; width: 278px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.019em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20514" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20515" class="mtable"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.142em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.902em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20516" class="mtd"><span id="MathJax-Span-20517" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20518" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20519" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20520" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20521" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20522" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20523" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20524" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20525" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20526" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20527" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20528" class="msubsup"><span style="display: inline-block; position: relative; width: 1.126em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20529" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20530" class="mi">m</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20531" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20532" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20533" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20534" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20535" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20536" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20537" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20539" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20540" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20541" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20542" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.281em; left: 0em;"><span id="MathJax-Span-20543" class="mtd"><span id="MathJax-Span-20544" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20545" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20546" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20547" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20548" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20550" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20551" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20552" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20553" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20554" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20555" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20556" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20557" class="msubsup"><span style="display: inline-block; position: relative; width: 1.126em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20558" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20559" class="mi">m</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20560" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20561" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20562" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20563" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20565" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20566" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20568" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20569" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20570" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20571" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20572" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20573" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20574" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20575" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20576" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.029em; left: 0em;"><span id="MathJax-Span-20577" class="mtd"><span id="MathJax-Span-20578" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20579" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20580" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20581" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20583" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20584" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20585" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.976em; vertical-align: -3.058em;"></span></span></nobr></span><script id="MathJax-Element-635" type="math/tex">\begin{array}[t]{l}
-\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
-\\
-\qquad r(id,a_1,\ldots,a_m) \wedge s(id,b_1,\ldots,b_n)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></div>
-<div class="proof">
- <p>This follows from the assumption that the different classes of
- interactions are disjoint sets, characterized by their types.
- </p>
- </div>
-<div class="constraint" number="54" id="impossible-object-property-overlap"><div class="ruleTitle"><a href="#impossible-object-property-overlap" class="internalDFN">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-636-Frame" class="MathJax"><nobr><span id="MathJax-Span-20586" class="math"><span style="display: inline-block; position: relative; width: 187px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.951em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20587" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20588" class="mi">p</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20589" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20590" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20592" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20594" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20596" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20597" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20598" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20599" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20600" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20601" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20602" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20603" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20604" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20605" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20606" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20607" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20608" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20610" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20612" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.073em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-636" type="math/tex">p \in \{entity,activity,agent\}</script> and each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-637-Frame" class="MathJax"><nobr><span id="MathJax-Span-20613" class="math"><span style="display: inline-block; position: relative; width: 1050px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20614" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20615" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20616" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20617" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20618" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20619" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20620" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20621" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20622" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20623" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20624" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20625" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20626" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20628" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20631" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20633" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20634" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20635" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20636" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20637" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20638" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20639" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20640" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20641" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20642" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20643" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20644" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20645" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20646" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20647" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20648" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20651" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20652" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20653" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20654" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20655" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20656" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20657" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20658" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20661" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; 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position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20798" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20800" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20801" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20802" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20804" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20805" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20806" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.057em; left: 0em;"><span id="MathJax-Span-20807" class="mtd"><span id="MathJax-Span-20808" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20809" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20810" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20811" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20812" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20813" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20814" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20815" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.006em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-638" type="math/tex">\begin{array}[t]{l}
-\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
-\\
-\qquad p(id,a_1,\ldots,a_m) \wedge r(id,b_1,\ldots,b_n)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></div>
-<div class="proof">
- <p>This follows from the assumption that interactions are distinct
- from other objects (entities, activities or agents).
- </p>
- </div>
-<div class="constraint" number="55" id="entity-activity-disjoint"><div class="ruleTitle"><a href="#entity-activity-disjoint" class="internalDFN">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-639-Frame" class="MathJax"><nobr><span id="MathJax-Span-20816" class="math"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.96em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20817" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20818" class="mtable"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(3.406em, 1000em, 7.024em, -0.526em); top: -4.264em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20819" class="mtd"><span id="MathJax-Span-20820" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20821" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20822" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20823" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20824" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20825" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-20826" class="mtd"><span id="MathJax-Span-20827" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20828" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20829" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20830" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20831" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20832" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20833" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20834" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20835" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20836" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20837" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20838" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20839" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20840" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20841" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20844" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20845" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20846" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20847" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20848" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20849" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20851" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20852" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20853" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20854" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20855" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20856" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20857" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20858" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20859" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20860" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20861" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20862" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20864" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20865" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: -0.03em; left: 0em;"><span id="MathJax-Span-20866" class="mtd"><span id="MathJax-Span-20867" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20868" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20869" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20870" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20871" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20872" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20873" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20874" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.264em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.913em; vertical-align: -2.994em;"></span></span></nobr></span><script id="MathJax-Element-639" type="math/tex">\begin{array}[t]{l}
-\forall id.~
-\\
-\qquad typeOf(id,entity) \wedge typeOf(id,activity)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></div>
-<div class="proof">
- <p>This follows from the assumption that entities and activities are disjoint.
- </p>
- </div>
-<div class="constraint" number="56" id="membership-empty-collection"><div class="ruleTitle"><a href="#membership-empty-collection" class="internalDFN">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-640-Frame" class="MathJax"><nobr><span id="MathJax-Span-20875" class="math"><span style="display: inline-block; position: relative; width: 419px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.034em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20876" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20877" class="mtable"><span style="display: inline-block; position: relative; width: 24.124em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.157em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.124em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20878" class="mtd"><span id="MathJax-Span-20879" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20880" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20881" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20882" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20883" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20884" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20885" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-20886" class="mtd"><span id="MathJax-Span-20887" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20888" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20889" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20890" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20891" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20892" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20893" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20894" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20895" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20896" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20897" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20898" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20899" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20900" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20901" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20902" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20903" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20905" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20906" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20907" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20908" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20909" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20910" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20911" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20912" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20913" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20914" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20915" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20916" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20917" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20918" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20919" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20920" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20921" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20922" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20923" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20924" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20925" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20926" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20927" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20928" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20930" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20931" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20932" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20933" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.044em; left: 0em;"><span id="MathJax-Span-20934" class="mtd"><span id="MathJax-Span-20935" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20936" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20937" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20938" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20939" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20940" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20941" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20942" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.992em; vertical-align: -3.073em;"></span></span></nobr></span><script id="MathJax-Element-640" type="math/tex">\begin{array}[t]{l}
-\forall c,e.~
-\\
-\qquad hasMember(c,e) \wedge typeOf(c,prov:EmptyCollection)
-\\
-\quad\Rightarrow
-False
-\end{array}</script></div>
-
-</section>
-</section>
-</section>
-
-
-<section id="soundness">
-<!--OddPage--><h2><span class="secno">6. </span>Soundness</h2>
-
-<p>Above we have presented arguments for the soundness of the
-constraints and inferences with respect to the reference semantics.
-This implies the following:
-
-</p><div data-title="Theorem 32 (soundness)" data-count="32" class="theorem" id="soundness"><div class="ruleTitle"><a href="#soundness" class="internalDFN">Theorem 32 (soundness)</a></div>
- <ol>
- <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-641-Frame" class="MathJax"><nobr><span id="MathJax-Span-20943" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20944" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20945" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-641" type="math/tex">I</script> is an instance and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-642-Frame" class="MathJax"><nobr><span id="MathJax-Span-20946" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20947" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20948" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20949" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20950" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-642" type="math/tex">W \models I</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-643-Frame" class="MathJax"><nobr><span id="MathJax-Span-20951" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20952" class="mrow"><span id="MathJax-Span-20953" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20954" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20955" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-643" type="math/tex">I'</script> is obtained from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-644-Frame" class="MathJax"><nobr><span id="MathJax-Span-20956" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20957" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20958" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-644" type="math/tex">I</script> by applying one
- of the PROV inferences, then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-645-Frame" class="MathJax"><nobr><span id="MathJax-Span-20959" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20960" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20961" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20962" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-20963" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20965" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-645" type="math/tex">W \models I'</script>.</li>
- <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-646-Frame" class="MathJax"><nobr><span id="MathJax-Span-20966" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20967" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20968" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-646" type="math/tex">I</script> is an instance and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-647-Frame" class="MathJax"><nobr><span id="MathJax-Span-20969" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20970" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20971" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20972" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20973" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-647" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-648-Frame" class="MathJax"><nobr><span id="MathJax-Span-20974" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20975" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20976" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-648" type="math/tex">I</script> has a normal
- form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-649-Frame" class="MathJax"><nobr><span id="MathJax-Span-20977" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20978" class="mrow"><span id="MathJax-Span-20979" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20980" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20981" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-649" type="math/tex">I'</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-650-Frame" class="MathJax"><nobr><span id="MathJax-Span-20982" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20983" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20984" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20985" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-20986" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20987" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20988" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-650" type="math/tex"> W \models I'</script>.</li>
- <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-651-Frame" class="MathJax"><nobr><span id="MathJax-Span-20989" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20990" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20991" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-651" type="math/tex">I</script> is a normal form and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-652-Frame" class="MathJax"><nobr><span id="MathJax-Span-20992" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20993" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20994" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20995" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20996" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-652" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-653-Frame" class="MathJax"><nobr><span id="MathJax-Span-20997" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20998" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20999" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-653" type="math/tex">I</script> satisfies all of the ordering,
- typing and impossibility constraints.
- </li><li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-654-Frame" class="MathJax"><nobr><span id="MathJax-Span-21000" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21001" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21002" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21003" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21004" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-654" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-655-Frame" class="MathJax"><nobr><span id="MathJax-Span-21005" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21006" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21007" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-655" type="math/tex">I</script> is valid.</li>
- <p></p>
-</ol></div>
-<div class="proof">
- <p>For part 1, the arguments are as in the previous section. </p>
- <p>For
- part 2, proceed by induction on a terminating sequence of inference
- or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-656-Frame" class="MathJax"><nobr><span id="MathJax-Span-21008" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21009" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21010" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-656" type="math/tex">I</script> is in normal form them we are
- done. If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-657-Frame" class="MathJax"><nobr><span id="MathJax-Span-21011" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21012" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21013" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-657" type="math/tex">I</script> is not in normal form then if an inference is applicable, then use part 1; if a uniqueness constraint is
- applicable, then from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-658-Frame" class="MathJax"><nobr><span id="MathJax-Span-21014" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21015" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21016" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21017" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21018" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-658" type="math/tex">W \models I</script> the uniqueness constraint cannot
- fail on <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-659-Frame" class="MathJax"><nobr><span id="MathJax-Span-21019" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21020" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21021" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-659" type="math/tex">I</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-660-Frame" class="MathJax"><nobr><span id="MathJax-Span-21022" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21023" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21024" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21025" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-21026" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21027" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21028" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-660" type="math/tex">W \models I'</script>.</p>
-<p>
- For part 3, the arguments are as
- in the previous section for each constraint. </p>
- <p>Finally, for part 4,
- suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-661-Frame" class="MathJax"><nobr><span id="MathJax-Span-21029" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21030" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21031" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21032" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21033" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-661" type="math/tex">W \models I</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-662-Frame" class="MathJax"><nobr><span id="MathJax-Span-21034" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21035" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21036" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21037" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-21038" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21039" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21040" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-662" type="math/tex">W \models I'</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-663-Frame" class="MathJax"><nobr><span id="MathJax-Span-21041" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-21042" class="mrow"><span id="MathJax-Span-21043" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21044" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21045" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-663" type="math/tex">I'</script> is the normal
- form of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-664-Frame" class="MathJax"><nobr><span id="MathJax-Span-21046" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21047" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21048" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-664" type="math/tex">I</script> by part 2. By part 3, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-665-Frame" class="MathJax"><nobr><span id="MathJax-Span-21049" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-21050" class="mrow"><span id="MathJax-Span-21051" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21052" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21053" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-665" type="math/tex">I'</script> satisfies all of the
- remaining constraints, so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-666-Frame" class="MathJax"><nobr><span id="MathJax-Span-21054" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21055" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21056" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-666" type="math/tex">I</script> is valid.</p>
- </div>
-
-
-
-</section>
-
-<section id="acknowledgements" class="appendix">
- <!--OddPage--><h2><span class="secno">A. </span>Acknowledgements</h2>
- <p>
-
-This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole.
- </p>
-<p>Thanks also to Robin Berjon for the ReSPec.js specification writing
-tool and to MathJax for their LaTeX-to-HTML conversion tools, both of
- which aided in the preparation of this document.</p>
-
-<p>
-Members of the PROV Working Group at the time of publication of this document were:
-
-Ilkay Altintas (Invited expert),
-Reza B'Far (Oracle Corporation),
-Khalid Belhajjame (University of Manchester),
-James Cheney (University of Edinburgh, School of Informatics),
-Sam Coppens (IBBT),
-David Corsar (University of Aberdeen, Computing Science),
-Stephen Cresswell (The National Archives),
-Tom De Nies (IBBT),
-Helena Deus (DERI Galway at the National University of Ireland, Galway, Ireland),
-Simon Dobson (Invited expert),
-Martin Doerr (Foundation for Research and Technology - Hellas(FORTH)),
-Kai Eckert (Invited expert),
-Jean-Pierre EVAIN (European Broadcasting Union, EBU-UER),
-James Frew (Invited expert),
-Irini Fundulaki (Foundation for Research and Technology - Hellas(FORTH)),
-Daniel Garijo (Universidad Politécnica de Madrid),
-Yolanda Gil (Invited expert),
-Ryan Golden (Oracle Corporation),
-Paul Groth (Vrije Universiteit),
-Olaf Hartig (Invited expert),
-David Hau (National Cancer Institute, NCI),
-Sandro Hawke (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="Massachusetts Institute of Technology">MIT</abbr>),
-Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
-Ivan Herman, (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>),
-Ralph Hodgson (TopQuadrant),
-Hook Hua (Invited expert),
-Trung Dong Huynh (University of Southampton),
-Graham Klyne (University of Oxford),
-Michael Lang (Revelytix, Inc.),
-Timothy Lebo (Rensselaer Polytechnic Institute),
-James McCusker (Rensselaer Polytechnic Institute),
-Deborah McGuinness (Rensselaer Polytechnic Institute),
-Simon Miles (Invited expert),
-Paolo Missier (School of Computing Science, Newcastle university),
-Luc Moreau (University of Southampton),
-James Myers (Rensselaer Polytechnic Institute),
-Vinh Nguyen (Wright State University),
-Edoardo Pignotti (University of Aberdeen, Computing Science),
-Paulo da Silva Pinheiro (Rensselaer Polytechnic Institute),
-Carl Reed (Open Geospatial Consortium),
-Adam Retter (Invited Expert),
-Christine Runnegar (Invited expert),
-Satya Sahoo (Invited expert),
-David Schaengold (Revelytix, Inc.),
-Daniel Schutzer (FSTC, Financial Services Technology Consortium),
-Yogesh Simmhan (Invited expert),
-Stian Soiland-Reyes (University of Manchester),
-Eric Stephan (Pacific Northwest National Laboratory),
-Linda Stewart (The National Archives),
-Ed Summers (Library of Congress),
-Maria Theodoridou (Foundation for Research and Technology - Hellas(FORTH)),
-Ted Thibodeau (OpenLink Software Inc.),
-Curt Tilmes (National Aeronautics and Space Administration),
-Craig Trim (IBM Corporation),
-Stephan Zednik (Rensselaer Polytechnic Institute),
-Jun Zhao (University of Oxford),
-Yuting Zhao (University of Aberdeen, Computing Science).
-</p>
- </section>
-
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-<div style="position: absolute; visibility: hidden; top: 0px; left: 0px; width: auto; padding: 0px; border: 0px none; margin: 0px; white-space: nowrap; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; font-size: 40px; font-weight: normal; font-style: normal; font-size-adjust: none; font-family: 'STIXSizeOneSym',sans-serif;" id="MathJax_Font_Test">ˆ</div><section class="appendix" id="references"><!--OddPage--><h2><span class="secno">B. </span>References</h2><section id="informative-references"><h3><span class="secno">B.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-Logic">[Logic]</dt><dd>W. E. Johnson. <a href="http://www.ditext.com/johnson/intro-3.html"><cite>Logic: Part III</cite></a>.1924. URL: <a href="http://www.ditext.com/johnson/intro-3.html">http://www.ditext.com/johnson/intro-3.html</a>
-</dd><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/"><cite>Provenance Access and Query</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">http://www.w3.org/TR/2013/WD-prov-aq-20130312/</a>
-</dd><dt id="bib-PROV-CONSTRAINTS">[PROV-CONSTRAINTS]</dt><dd>James Cheney; Paolo Missier; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/"><cite>Constraints of the PROV Data Model</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">http://www.w3.org/TR/2013/PR-prov-constraints-20130312/</a>
-</dd><dt id="bib-PROV-DC">[PROV-DC]</dt><dd>Daniel Garijo; Kai Eckert; eds. <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/"><cite>Dublin Core to PROV Mapping</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">http://www.w3.org/TR/2013/WD-prov-dc-20130312/</a>
-</dd><dt id="bib-PROV-DICTIONARY">[PROV-DICTIONARY]</dt><dd>Tom De Nies; Sam Coppens; eds. <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/"><cite>PROV Dictionary</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/</a>
-</dd><dt id="bib-PROV-DM">[PROV-DM]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/"><cite>PROV-DM: The PROV Data Model</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">http://www.w3.org/TR/2013/PR-prov-dm-20130312/</a>
-</dd><dt id="bib-PROV-LINKS">[PROV-LINKS]</dt><dd>Luc Moreau; Timothy Lebo; eds. <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/"><cite>Linking Across Provenance Bundles</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">http://www.w3.org/TR/2013/WD-prov-links-20130312/</a>
-</dd><dt id="bib-PROV-N">[PROV-N]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/"><cite>PROV-N: The Provenance Notation</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">http://www.w3.org/TR/2013/PR-prov-n-20130312/</a>
-</dd><dt id="bib-PROV-O">[PROV-O]</dt><dd>Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/"><cite>PROV-O: The PROV Ontology</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">http://www.w3.org/TR/2013/PR-prov-o-20130312/</a>
-</dd><dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Paul Groth; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/"><cite>PROV-OVERVIEW: An Overview of the PROV Family of Documents</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">http://www.w3.org/TR/2013/WD-prov-overview-20130312/</a>
-</dd><dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/"><cite>PROV Model Primer</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">http://www.w3.org/TR/2013/WD-prov-primer-20130312/</a>
-</dd><dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James Cheney; ed. <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312"><cite>Semantics of the PROV Data Model</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312">http://www.w3.org/TR/2013/WD-prov-sem-20130312</a>.
-</dd><dt id="bib-PROV-XML">[PROV-XML]</dt><dd>Hook Hua; Curt Tilmes; Stephan Zednik; eds. <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">http://www.w3.org/TR/2013/WD-prov-xml-20130312/</a>
-</dd></dl></section></section></body></html>
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--- a/semantics/prov-sem.html Fri Mar 01 17:58:46 2013 +0000
+++ b/semantics/prov-sem.html Fri Mar 01 18:04:49 2013 +0000
@@ -70,7 +70,7 @@
background: #fff;
}
-.formalism {
+.semantics {
padding: 1em;
margin: 1em 0em 0em;
border: 1px solid #0f0;
@@ -96,7 +96,7 @@
.proof {
padding: 1em;
margin: 1em 0em 0em;
- border: 1px solid #888;
+ border: 1px dotted #888;
background: #FFFFFF;
}
.proof::before {
@@ -110,7 +110,13 @@
padding: 3px 1em;
}
-
+.proof::after {
+ content: "QED";
+ display: block;
+ text-align: right;
+ font-weight: bold;
+ padding: 3px 1em;
+}
/* .inference[id]::before { */
/* content: "Inference: " attr(id); */
@@ -614,7 +620,7 @@
function updateRules() {
var count=1;
- $('.constraint,.definition,.inference,.formalism,.component,.theorem').each(function(index) {
+ $('.constraint,.definition,.inference,.semantics,.component,.theorem').each(function(index) {
var myid=$(this).attr('id');
var mycount=$(this).attr('number');
@@ -1255,9 +1261,7 @@
</p>
<p>Each parameter is either an identifier, a constant (e.g. a time or
other literal value in an attribute list), or a null symbol "-".
- Time parameters ($st,et$ in $activity$, and $t$ in generation,
- usage, invalidation, start and end) are always constant time
- literals. Placeholder symbols $-$ can only appear in the specified arguments
+ Placeholder symbols $-$ can only appear in the specified arguments
$pl$ in $wasAssociatedWith$ and $a,g,u$ in $wasDerivedFrom$, as shown in the grammar below.
</p>
$$
@@ -1384,7 +1388,7 @@
<p>The identity of a Thing is not observable through its attributes or
-lifetime, so it is possible for two different Things to be indistinguishable by their
+lifetime, so it is possible for two different $Things$ to be indistinguishable by their
attribute values and lifetime. That is, if the set of $Things = \{T_0,T_1\}$ and the attributes are
specified as $value(T_0,a,t) = value(T_1,a,t)$ for each $t\in
Times$ and $a \in Attributes$, this does not imply that $T_0 = T_1$.
@@ -1731,7 +1735,7 @@
the standard definition of the semantics of the other formulas:
</p>
-<div class="formalism" id="first-order-logic">
+<div class="semantics" id="first-order-logic-semantics">
<ol>
<li>$W,\rho \models True$ always holds.</li>
<li>$W,\rho \models False$ never holds.</li>
@@ -1794,7 +1798,7 @@
</p>
<p>Entity formulas $entity(id,attrs)$ can be interpreted as follows:
</p>
-<div class="formalism">
+<div class="semantics" id="entity-semantics">
<p>$W,\rho \models entity(id,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $id$ denotes an entity $ent = \rho(id) \in Entities$
@@ -1832,15 +1836,15 @@
time and $et$ is an end time, and $attrs$ are the attributes of
activity $id$.
</p>
-<div class="formalism">
+<div class="semantics" id="activity-semantics">
<p>$W,\rho \models activity(id,st,et,attrs)$
holds if and only if:</p>
<ol>
<li>[WF] The identifier $id$ maps to an activity $act = \rho(id) \in Activities$
</li>
-<li>$st$ is the activity's start time, that is: $min(lifetime(id)) = st$
+<li>$\rho(st) \in Times$ is the activity's start time, that is: $min(lifetime(id)) = \rho(st)$
</li>
-<li>$et$ is the activity's end time, that is: $max(lifetime(id)) = et$
+<li>$\rho(et)$ is the activity's end time, that is: $max(lifetime(id)) = \rho(et)$
</li>
<li>The attributes match: $match(W,act,attrs)$.
</li>
@@ -1853,7 +1857,7 @@
<p>An agent formula is of the form $agent(id,attrs)$ where $id$ denotes the agent and $attrs$ describes additional attributes.
</p>
-<div class="formalism">
+<div class="semantics" id="agent-semantics">
<p>$W,\rho \models agent(id,attrs)$ holds if and only if:
</p>
<ol>
@@ -1878,7 +1882,7 @@
$e$ is an entity identifier, $a$ is an activity identifier, $attrs$ is
a set of attribute-value pairs, and $t$ is a time.
</p>
-<div class="formalism">
+<div class="semantics" id="generation-semantics">
<p>$W,\rho \models
wasGeneratedBy(id,e,a,t,attrs)$ holds if and only if:</a>
<ol>
@@ -1892,7 +1896,7 @@
</li>
<li>The type of $evt$ is $generation$, i.e. $type(evt) = generation$.
</li>
-<li>The event $evt$ occurred at time $t$, i.e. $time(evt) = t$.
+<li>The event $evt$ occurred at time $\rho(t) \in Times$, i.e. $time(evt) = \rho(t)$.
</li>
<li>The event $evt$ generated $ent$, i.e. $(evt,ent) \in Generated$.
</li>
@@ -1907,7 +1911,7 @@
<p>The use formula is of the form $used(id,a,e,t,attrs)$ where $id$ denotes an event, $a$ is an activity identifier, $e$ is an object identifier, $attrs$ is a set of attribute-value pairs, and $t$ is an optional time.
</p>
-<div class="formalism">
+<div class="semantics" id="usage-semantics">
<p>$W,\rho \models used(id,a,e,t,attrs)$ holds if and only if:</p>
<ol>
</li>
@@ -1921,7 +1925,8 @@
</li>
<li>The type of $evt$ is $use$, i.e., $type(evt) = use$.
</li>
-<li>The event $evt$ occurred at time $t$, i.e. $time(evt) = t$.
+<li>The event $evt$ occurred at time $\rho(t) \in Times$,
+i.e. $time(evt) = \rho(t)$.
</li>
<li>The event $evt$ used $obj$, i.e. $(evt,ent) \in Used$.
</li>
@@ -1934,7 +1939,7 @@
<p>The invalidation formula is of the form $wasInvalidatedBy(id,e,a,t,attrs)$ where $id$ is an event identifier, $e$ is an entity identifier, $a$ is an activity identifier, $attrs$ is a set of attribute-value pairs, and $t$ is an optional time.</p>
-<div class="formalism"> <p>An invaliation formula $W,\rho \models
+<div class="semantics" id="invalidation-semantics"> <p>An invalidation formula $W,\rho \models
wasInvalidatedBy(id,e,a,t,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] The identifier $id$ denotes an event $evt = \rho(id) \in Events$.
@@ -1947,7 +1952,8 @@
</li>
<li>The type of $evt$ is $invalidation$, i.e. $type(evt) = invalidation$.
</li>
-<li>The event $evt$ occurred at time $t$, i.e. $time(evt) = t$.
+<li>The event $evt$ occurred at time $\rho(t) \in Times$,
+ i.e. $time(evt) = \rho(t)$.
</li>
<li>The event $evt$ invalidated $ent$, i.e. $(evt,ent) \in Invalidated$.
</li>
@@ -1961,7 +1967,7 @@
<p>An association formula has the form $wasAssociatedWith(id,a,ag,pl,attrs)$.</p>
-<div class="formalism"><p>
+<div class="semantics" id="association-plan-semantics"><p>
$W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $assoc$ denotes an association $assoc = \rho(id) \in Associations$.
@@ -1977,7 +1983,7 @@
<li>The attributes match: $match(W,assoc,attrs)$.
</li></ol></div>
-<div class="formalism"><p>
+<div class="semantics" id="assocation-semantics"><p>
$W,\rho \models wasAssociatedWith(id,a,ag,-,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $assoc$ denotes an association $assoc = \rho(id) \in Associations$.
@@ -1996,7 +2002,7 @@
<p>A start formula $wasStartedBy(id,a_2,e,a_1,t,attrs)$ is interpreted as follows:</p>
-<div class="formalism">
+<div class="semantics" id="start-semantics">
<p>$W,\rho \models wasStartedBy(id,a_2,e,a_1,t,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $id$ denotes an event $evt = \rho(id) \in Events$.
@@ -2010,7 +2016,7 @@
<li>The event $evt$ has type $start$, i.e. $type(evt) = start$.
</li>
<li>The event happened at the start of $act_2$, that is, $(evt,act_2)
- \in EventsActivities$, and $t = min(lifetime(act_2)) = time(evt)$.
+ \in EventsActivities$, and $\rho(t) = min(lifetime(act_2)) = time(evt)$.
</li>
<li>TODO: The entity $e$ was generated by $act_1$ and started $act_2$.
<li>The event happened during $act_1$, that is, $(evt,act_1)
@@ -2024,7 +2030,7 @@
<p>An activity end formula $wasEndedBy(id,a_2,e,a_1,t,attrs)$ is interpreted as follows:</p>
-<div class="formalism">
+<div class="semantics" id="end-semantics">
<p>
$W,\rho \models wasEndedBy(id,a_2,e,a_1,t,attrs)$ holds if and only
if:</p>
@@ -2036,7 +2042,7 @@
<li>[WF] $a_1$ denotes an activity $act_1 = \rho(a_1)\in Activities$.</li>
<li>The event $evt$ has type $end$, i.e. $type(evt) = end$.</li>
<li>The event happened at the end of $act_2$, that is, $(evt,act_2)
- \in EventsActivities$, and $t = max(lifetime(act_2)) = time(evt)$.</li>
+ \in EventsActivities$, and $\rho(t) = max(lifetime(act_2)) = time(evt)$.</li>
<li>TODO: The entity $e$ was generated by $act_1$ and ended $act_2$.</li>
<li>The event happened during $act_1$, that is, $(evt,act_1) \in EventActivity.</li>
@@ -2051,7 +2057,7 @@
<p>
An attribution formula $wasAttributedTo(id,e,ag,attrs)$ is interpreted as follows:
</p>
-<div class="formalism">
+<div class="semantics" id="attribution-semantics">
<p>
$W,\rho \models wasAttributedTo(id,e,ag,attrs)$
holds if and only if:
@@ -2084,11 +2090,11 @@
<section>
-<h5> Responsibility </h5>
+<h5> Delegation </h5>
<p>The $actedOnBehalfOf(id,ag_2,ag_1,act,attrs)$ relation is interpreted using the $ActsFor$ relation as follows:</p>
-<div class="formalism">
+<div class="semantics" id="delegation-semantics">
<p>
$W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)$ holds if and only if:</p>
<ol>
@@ -2124,7 +2130,7 @@
<p>A precise derivation formula has the form $wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)$.
</p>
-<div class="formalism">
+<div class="semantics" id="derivation-precise-semantics">
<p>$W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $id$ denotes a derivation $deriv = \rho(id) \in Derivations$.
@@ -2150,7 +2156,7 @@
<p>
An imprecise derivation formula has the form $wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)$.</p>
-<div class="formalism">
+<div class="semantics" id="derivation-imprecise-semantics">
<p>$W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)$ holds if and only if:</p>
<ol>
<li>[WF] $id$ denotes a derivation $deriv = \rho(id) \in Derivations$
@@ -2182,7 +2188,7 @@
itself this definition is not transitive.</p>
</div>
-<div class="formalism"> <p>
+<div class="semantics" id="specialization-semantics"> <p>
$W,\rho \models specializationOf(e_1,e_2)$ holds if and only if:</p>
<ol>
<li>[WF] Both $e_1$ and $e_2$ are entity identifiers, denoting
@@ -2211,7 +2217,7 @@
<p>The $alternateOf$ relation indicates when two entity formulas present (possibly different) aspects of the same thing. The two entities may or may not overlap in time.
</p>
-<div class="formalism">
+<div class="semantics" id="alternate-semantics">
<p>
$W,\rho \models alternateOf(e_1,e_2)$ holds if and only if:</p>
<ol>
@@ -2231,7 +2237,7 @@
<p>The $hadMember$ relation relates a collection to an element of the collection.
</p>
-<div class="formalism">
+<div class="semantics" id="membership-semantics">
<p>
$W,\rho \models hadMember(c,e)$ holds if and only if:</p>
<ol>
@@ -2262,7 +2268,7 @@
<h4>Equals</h4>
<p>As usual, an equality formula means that two expressions denote
the same value. Identifiers always denote $Objects$.</p>
- <div class="formalism" id="equality">
+ <div class="semantics" id="equals-semantics">
<p>$W,\rho \models x = y$ holds if and only if $\rho(x) =
\rho(y)$.</p>
</div>
@@ -2276,7 +2282,7 @@
mapped to a single time line, this amounts to
comparing the event times. The semantics of strictly precedes ($x
\prec y$ is similar, only $x$ must take place strictly before $y$).</p>
- <div class="formalism" id="precedes">
+ <div class="semantics" id="precedes-semantics">
<ol>
<li>$W,\rho \models x \preceq y$ holds if and only if
$\rho(x),\rho(y) \in Events$ and $time(\rho(x)) \leq time(\rho(y))$.</li>
@@ -2308,12 +2314,14 @@
<p>The $notNull(x)$ formula is used to specify that a value may not
be the null value $\bot$. The symbol $-$ always denotes the null
value (i.e. $\rho(-) = \bot$).
- <div class="formalism" id="notNull">
+ <div class="semantics" id="notNull-semantics">
<p>$W,\rho\models notNull(e)$ holds if and only if $e \neq
\bot$.
</p>
</div>
-
+
+ <div class="note">
+ This can be defined as $\neg (x=\bot)$.
</section>
<section>
@@ -2322,7 +2330,7 @@
<p>The typing formula $typeOf(x,t)$ constrains the type of the value of
$x$. </p>
- <div class="formalism" id="typeOf">
+ <div class="semantics" id="typeOf-semantics">
<ol><li>$W,\rho\models typeOf(e,entity)$ holds if and only if
$\rho(e) \in Entities$.</li>
<li>$W,\rho\models typeOf(a,activity)$ holds if and only if
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/ISSUE-630-khalid.txt Fri Mar 01 18:04:49 2013 +0000
@@ -0,0 +1,109 @@
+ > 1. Is the purpose of the document clear and consistent with the
+ > working group's consensus about the semantics? If not, can you
+ > suggest clarifications or improvements?
+ >
+ > Yes.
+ >
+ >
+ > 2. Are there minor issues that can be corrected easily prior to FPWD release?
+ >
+ > Yes, I am listing them below.
+ >
+ > 2.1 In component 1 (things). The second bullet states that "a function
+ > lifetime:Things→Intervals from objects to time intervals". Shouldnt it
+ > be "from things to time intervals"?
+
+Yes, fixed.
+
+ >
+ > 2.2 In section 3.2, I think it would be good to add text explaining
+ > the relationship between Things and Objects, before definition
+ > Objects.
+
+TODO
+
+ >
+ > 2.3 In the definition of Component 10 (derivations), I think version
+ > should be replaced by revision.
+
+Done
+
+ >
+ > 2.4 In Section 3.3, when listing simple relations, the variable "g" is
+ > not introduced. Actually I think you meant to use "evt" instead.
+
+Fixed
+
+ >
+ > 2.5 In the same section, in the first bullet "use" should be replaced
+ > by "usage" as this was the term used when defining events in component
+ > 8 (events).
+
+Fixed
+
+ >
+ > 2.5 In the same section, there is an error in talking about
+ > invalidation (bullet 3), min(lifetime(e)) = time(evt) should be
+ > modified to max(lifetime(e)) = time(evt)
+
+Fixed
+
+ >
+ > 2.6 The document makes distinguishes between precise and iprecise
+ > derivation, and refer to "Imprecise wasDerivedFrom". PROV-DM does not
+ > makes that distinction anymore. I think distinguishing the two is
+ > worthwile in ProvSem. So here the suggestion is add a sentence or two
+ > introducing the two kinds of derivation and not referring to the
+ > PROV-DM.
+
+Fixed
+
+ >
+ > 2.7 In the proof of inference 16, inference 17 and inference 18,
+ > "rho(e1)" should be replaced by "p(e1)".
+ >
+
+Fixed
+
+ >
+ > 3. Are there blocking issues that must be addressed prior to release
+ > as a first public working draft?
+ >
+ >
+ > There are no blocking issues before release as a first public working draft.
+ >
+ >
+ > 4. Are there non-blocking, but important issues that should be
+ > discussed and resolved for future editions? (no need to list TODOs
+ > already reflected in the document itself, unless there is disagreement
+ > about how to resolve them).
+ >
+ > The following comments can be included later on. They are by no mean blocking.
+ >
+ > 4.1 I noticed that bundles are not mentioned in the document. Is there
+ > a reason for that?
+
+Yes; this is now addressed in the introduction. See also Luc's comment.
+
+ >
+ > 4.2 In the definition of Component 3 (entities), the function thingOf
+ > is used to associate Entities with Things. Is there any reason why
+ > such a function is not generalized to associate Objects with Things?
+
+No, but there is no need for it either. The only relations that involve the thingOf function are specialization and alternate, which can only be used on entities.
+
+ >
+ > 4.3 The derivation path (Section 3.3.1) is defined as
+ > DerivationPaths=Entities⋅(Events⋅Activities⋅Events⋅Entities)+ I this
+ > this can be more specific by identifying the kind of events, whether
+ > they are generation or usage. This suggestion will require introducing
+ > a new sets that are subsets of Events, namely Generations and Usages.
+ >
+
+TODO
+
+ > 4.4 In the formulas defining the semantics of the relation sin Section
+ > 4.4, place hoder parameters are not specified.
+ >
+
+Fixed - now there are two formalism boxes.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/ISSUE-630-luc.txt Fri Mar 01 18:04:49 2013 +0000
@@ -0,0 +1,115 @@
+
+ > - sotd pagraph: (this document) is on prov-constraints, and self reference to [prov-sem] to be removed.
+ >
+
+Done
+
+ > - section 2.2: for convenience, we assume the order is total. What is the implication of this choice?
+
+Raised ISSUE-635
+ >
+ > - section 2.4: wasStartedBy/wasEndedBy are missing time
+
+Fixed
+
+ >
+ > - section 2.4: no bundle here? Shouldnt' we? or too slippery topic?
+
+Added some explanation of this in the introduction [TODO]
+
+ >
+ > - section 2.5: could the final version have a go at an interpretation of mentionOf, even if marked as more speculative and in appendix?
+
+I would prefer to avoid this. If there's time maybe.
+
+ >
+ > - section 3.2: term interaction not defined yet.
+
+Fixed
+
+ >
+ > - section 3.2.1: Can we provide some intution for value(obj,a) \subseteq value(thingOf(obj),a,t). What does it tell us about entities vs things.
+
+TODO
+
+ >
+ > - section 3.2.4: (the first two sets may overlap) which? Why?
+
+Fixed - this remark was out of date.
+
+ > Events is not defined yet.
+
+Fixed - it's a forward reference to later in the section
+
+ >
+ > - section 3.2.4.1: lifetime(evt)={time(t)} isn't it time(evt)?
+
+Fixed
+
+ >
+ > - section 3.3: EventActivity I think allows for an event not to be associated with any activity. Is this desirable?
+
+It's tru that this is allowed. We could make it a function, since every event is associated with exactly one activity. At the time this was written this wasn't clear.
+
+ >
+ > - 3.3.1: function derivedFrom linking each derivation to ITS path:
+ > I would suggest
+ > function derivedFrom linking each derivation to SOME path.
+ > in the case wasDerivedFrom(e1,e2,-,-,-) there may be multiple paths.
+ >
+
+True, but since we are always considering formulas that specify an identity for the derivation relationship, I believe each distinct derivation has its own path. I added a remark to this effect.
+
+ >
+ > - section 4.3.1: we could add some intution: not all attributes of an
+ > entity object are required to be present in an entity formula.
+
+Done
+
+ >
+ > - 4.3.2, rule_13:
+ > "if st is specified", what do you mean? st is always present as a constant or variable. Do you mean "if st is a variable"?
+ > How do we have to read min(lifetime(id))=st if st is variable?
+
+Fixed. A time can potentially be a variable if it is omitted and then expanded to an existential variable. So we need to write rho(t) when we need its value.
+
+ >
+ > Elsewhere, when time occurs in a formula, there is no clause "if t is specified".
+ > Why this differnce?
+
+Fixed, this phrasing was outdated.
+
+ >
+ > - formalism 16: who do we read time(evt)=t when t is variable?
+
+Fixed, now reads rho(t)
+
+ >
+ > - 4.4.7: nothing in the semantics seems to indicate that lifetime of
+ > agent precedes that of entity.
+
+This constraint (and a number of other constraints) are not yet reflected in the semantics. They will be, but doing this is somewhat repetitive, and I'm undecided as to the best way to do it. This can be discussed under ISSUE-635.
+
+ >
+ > - 4.4.12: there is some occurrence of obj_1/obj_2 which should be ent_1/ent_2
+ >
+
+Fixed
+
+ > - formalism 29 (precedes)
+ >
+ >
+ > entity(e)
+ > activity(a1)
+ > activity(a2)
+ > wasGeneratedBy(gen1; e, a1, 2011-11-16T16:05:00)
+ > wasGeneratedBy(gen2; e, a2, 2012-11-16T16:05:00) //different date
+ >
+ >
+ > gen1 <= gen2 and gen2 <= gen1
+ >
+ >
+ > Formalism 29 implies: 2011-11-16T16:05:00 == 2012-11-16T16:05:00
+ > (see separate email)
+
+Raised ISSUE-635
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/ISSUE-630-paolo.txt Fri Mar 01 18:04:49 2013 +0000
@@ -0,0 +1,81 @@
+ > ====
+ > Minor issues:
+ > ====
+ >
+ > 1.1. " It is intended as an exploration of a reference semantics for PROV, not a definitive specification of the only semantics of PROV."
+ > this may be too defensive?: it seems to imply that there may be other semantics of PROV but in that case it is not clear where sand when they would come from, and thus whether using this document is "safe".
+ >
+
+Following comments from Luc, I think it is important to delimit the scope of the document. It is not a specification and we don't want to make it sound like it is doing more than it is. TODO
+
+ > 1.2 final note: not sure what this refers too -- assume it's for internal use only.
+
+Clarified this
+
+ >
+ > 3.
+ >
+ > 3.1
+ > "Things are things in the world." some may find this a bit tautologic? since you give examples of Objects, why not give examples of Things too here, this would actually help appreciate the sharp distinction between the two that you make in 3.2 ("objects are not things...").
+ > Use of term "object" before 3.2 may be confusing
+
+Fixed. The examples are actually examples of Things; the notation was inconsistent.
+
+ >
+ > 3.2
+ > "An Object is described by a time interval and attributes with unchanging values." would adding "within that time interval" clarify the distinction between things and objects? (and would it be correct)
+
+Rephrased this
+
+ >
+ > "however, certain objects, namely entities, are linked to things." "linked to" seems deliberately weak -- is it too strong to say that entities can be representations of things?
+
+We had a lot of discussions about whether objects/entities represent things and I didn't want to reopen that worm can. I'd prefer a weaker statement about the structures, that doesn't have as much baggage.
+
+ >
+ > 3.2.4.5 Derivations
+ > "chaining one or more generation and use steps." this may lead to incorrect inference assumptions (that from use/gen you can infer derivations). Since this is clarified in 4.4.10, maybe put a ref to it?
+
+Well, we don't say that a generation + use step implies a derivation step anywhere. I've added a remark clarifying this.
+
+ >
+ > 4.4.10 (also remark in 3.3.1) the terms "precise" and "imprecise" are not from PROV-DM, indeed not in CONSTR either. But in CONSTR inference 11 effectively requires derivation to be preciseI. it may be worth unifying the terminology?
+
+Added a remark clarifying this.
+
+ >
+ > 6 I think the terms "normal form" and "valid" only appear here (and in 1.1 -- purpose). It may be useful to recall their meaning here from the constraints doc?
+ >
+
+Highlighted the uses of the terms and referred to prov-constraints.
+
+ >
+ >
+ > typos / gremlins:
+ >
+ > - mix of italics/ plain font:
+ > "alternateOf and specializationOf relations" in 1.1
+ > "We write Identifiers for the set of identifiers" in 2.1 etc
+
+This is intentional, italic typeface is used for mathematical notation a la LaTeX and so these refer to relation or set names. There are places where capitalized words aren't italicized and should be, which I'll try to fix.
+
+ > prints cramped in my rendering, and looks cramped too in the browser
+ >
+
+It is difficult to get the rules to print out cleanly in a systematic way, since mathML seems to render on one line by default. I will try to fix this in future versions.
+
+ > - abstract: on use -> on the use
+ >
+ > 3.2.1 remark "orthe associated thing"
+ >
+ > 3.2.4.1 "invalidation} if and only of evt∈Events." (partially unreadable, of -> if)
+ >
+ > 3.3 bullet point 5: Association -> Associations
+ >
+ > 3.3., 3.3.1 EventActivity/ EventActivities
+ >
+ >
+ > 5.1 onwards: a few rho --> \rho gremlins in Proofs
+ >
+
+All fixed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/ISSUE-630-satya.txt Fri Mar 01 18:04:49 2013 +0000
@@ -0,0 +1,72 @@
+
+ > Review questions:
+ >
+ > 1. Is the purpose of the document clear and consistent with the working group's consensus about the semantics? If not, can you suggest clarifications or improvements?
+ >
+ > Yes (couple points for clarification listed below)
+ >
+ > 2. Are there minor issues that can be corrected easily prior to FPWD release?
+ >
+ > Yes
+ >
+ > 3. Are there blocking issues that must be addressed prior to release as a first public working draft?
+ >
+ > No
+ >
+ > 4. Are there non-blocking, but important issues that should be discussed and resolved for future editions? (no need to list TODOs already reflected in the document itself, unless there is disagreement about how to resolve them).
+ >
+ > Possibly some points need discussions
+ >
+ > My comments:
+ >
+ > Section 2.1
+ > a) "Identifiers are viewed as variables in logic (or blank nodes in RDF)" - Not clear about reference to blank nodes in RDF (they are existentially qualified identifiers?)
+ >
+
+Removed the probably confusing reference to RDF (since you're right that variables need not be solely existential here).
+
+ > Section 3.1:
+ > a) "An object could just be a record of fixed attribute values; it could be a bear; it could be the Royal Society; it could be a transcendental number like ..." - object is used in description of Thing - typo?
+
+Fixed
+
+ >
+ > b) "It is possible for two Things to be indistinguishable by their attribute values and lifetime, but have different identity." - Is there one Thing with two identities, if there are two Things it would be natural to have two identity? Maybe some clarification will help.
+ >
+
+By "identity" I mean an element of the set of things. This passage was confusing and I changed it to clarify what I am trying to say: basically, two different things can be indistinguishable in terms of their attributes and lifespan withoug being identical.
+
+ > c) It is not clear why we need a strict disjointness constraint for object and Thing.
+ >
+
+It is not necessary anywhere, but I think it is less confusing to keep the two sets separate (and this doesn't stop us from doing anything as far as I can see). Otherwise, say x in Object intersect Thing, then could it have different lifespans according to whether we consider it an object or a thing?
+
+ > c) "Objects encompass entities, interactions, and activities." - Then we don't need to list "agent" explicitly for range of quantifiers in Section 4.1 (Remarks), Section 3.2.4 (Component 7 (4))
+ >
+
+Fixed this inconsistency - Objects include entities, activities, agents and interactions everywhere now.
+
+ > Section 3.2.3
+ > a) " An agent can be an entity, an activity, or neither; ..." Not clear about "neither"
+ >
+
+There is nothing in PROV-DM or PROV-CONSTRAINTS to say that an agent must be an entity or an activity, only that some agents might be entities or activities (but not both).
+
+ > Section 3.2.4
+ > a) Not clear why the Associations, Communications etc. have to be disjoint?
+
+This is to match constraint 53.
+
+ >
+ > Section 3.3.1
+ > a) DerivationPaths=Entities⋅(Events⋅Activities⋅Events⋅Entities) - We can replace Events by Generation and Used directly since the following constraints specifies only one replacement for Events?
+ >
+
+TODO
+
+ > Minor Typos:
+ > Section 3.2.2 Actvities/Activities
+ > Section 4.4.12 "...two entities present aspects of the same Thing..."/"...two entities present different aspects of the same Thing..."
+ > Section 5.1 Inference 17 "alternateOf(e_2, e_1)$"/ "alternateOf(e_1,e_3)$
+
+Fixed.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/semantics/review/ISSUE-630-simon.txt Fri Mar 01 18:04:49 2013 +0000
@@ -0,0 +1,66 @@
+1. Is the purpose of the document clear and consistent with the working group's consensus about the semantics?
+ >
+ > Yes.
+ >
+ >
+ > 2. Are there minor issues that can be corrected easily prior to FPWD release?
+ >
+ > You refer to "PROV instance" a few times. Should this be "PROV document"?
+ >
+
+I meant instance, since that is the level of granularity that corresponds to a theory/model. Documents can be handled by treating each instance separately. I don't propose to try to model bundles or linking relations among them.
+
+ > In the grammar at the start of Sec 2.4 (and at least once later), why have Collection and EmptyCollection got prov: prefixes unlike any other term?
+
+Because these are the type names used in PROV-CONSTRAINTS. As far as I am aware there is no reason for them to have prefixes there either but no one objected to it. The type names don't actually matter very much.
+
+ >
+ > Typo in Remark in Section 3.2.1: "forthe"
+
+Fixed
+
+ >
+ > Section 3.2.1: "An entity is a kind of object... the entity does not record a fixed value for a" - doesn't sound right. What does it mean for an object to record something?
+
+Fixed (the entity now just "has" attributes /values)
+
+ >
+ > Section 3.2.3: I notice that the description of agents does not refer to responsibility, which is the key concept in DM.
+
+Copied over the current text - the existing text was way out of date. This is probably also true elsewhere.
+
+ >
+ > Typo in Section 3.2.4.1: In line 1 of the definition, "if and only of evt"
+
+Fixed
+
+ >
+ > The precedes relation does not appear correctly in my browser (other symbols render fine).
+ >
+
+This can be fixed by improving Unicode support...
+
+ >
+ > 3. Are there blocking issues that must be addressed prior to release as a first public working draft?
+ >
+ > No.
+ >
+ >
+ > 4. Are there non-blocking, but important issues that should be discussed and resolved for future editions? (no need to list TODOs already reflected in the document itself, unless there is disagreement about how to resolve them).
+ >
+ > Section 3.2.4: You say that Events and Associations may overlap, but the function type() seems to preclude that: if an interaction is in Associations, it has type association, but that is not an allowed type for a member of Events?
+
+The suggestion that they may overlap was unintended (carried over from an earlier version); fixed.
+
+ >
+ > Section 3.3.1: "linking each derivation to its path" - I'm not clear why a derivation maps to just one path.
+
+See also response to Luc. This is a modeling choice, not a derived property, but note that you can have multiple derivation relations (with different identifiers) linking two entities. So there is no loss of generality in supposing that each has its own path.
+
+ >
+ > A lot of Section 4 seems to be making "obvious" connections between structures and the relations of Section 3. Might the amount of text obscure the parts that are most interesting and not necessarily intuitive, e.g. in the definitions of precise derivation (single step derivation path), specialization and alternate (common things between entities)? Could these special features of the semantics be highlighted in some way?
+ >
+
+This is a good point; a lot of the semantics is just restating the constraints in a different notation, as can often be the case with semantics. The derivation paths and Thing/Entity/thingOf structure is more interesting and should be highlighted. I'd ideally like to avoid saying the same thing several different ways but not sure yet how best to do this.
+
+TODO: Highlight the distinctive components
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
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+ <body><div class="head">
+ <p>
+
+ <a href="http://www.w3.org/"><img src="https://www.w3.org/Icons/w3c_home" alt="W3C" height="48" width="72"></a>
+
+ </p>
+ <h1 class="title" id="title">Semantics of the PROV Data Model</h1>
+
+ <h2 id="w3c-editor-s-draft-25-february-2013"><abbr title="World Wide Web Consortium">W3C</abbr> Editor's Draft 25 February 2013</h2>
+ <dl>
+
+ <dt>This version:</dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
+ <dt>Latest published version:</dt>
+ <dd><a href="http://www.w3.org/TR/prov-sem/">http://www.w3.org/TR/prov-sem/</a></dd>
+
+
+ <dt>Latest editor's draft:</dt>
+ <dd><a href="http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html">http://dvcs.w3.org/hg/prov/raw-file/default/semantics/prov-sem.html</a></dd>
+
+
+
+
+
+
+
+
+ <dt>Editor:</dt>
+ <dd><a href="http://homepages.inf.ed.ac.uk/jcheney">James Cheney</a>, University of Edinburgh</dd>
+
+
+ </dl>
+
+
+
+
+
+ <p class="copyright">
+ <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> ©
+ 2012-2013
+
+ <a href="http://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
+ (<a href="http://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
+ <a href="http://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
+ <a href="http://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>), All Rights Reserved.
+ <abbr title="World Wide Web Consortium">W3C</abbr> <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
+ <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and
+ <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.
+ </p>
+
+
+ <hr>
+</div><div style="visibility: hidden; overflow: hidden; position: absolute; top: 0px; height: 1px; width: auto; padding: 0px; border: 0px none; margin: 0px; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal;"><div id="MathJax_Hidden"></div></div><div style="display: none;" id="MathJax_Message"></div>
+
+ <section class="introductory" id="abstract"><h2>Abstract</h2>
+<p>
+Provenance is information about entities, activities, and people
+involved in producing a piece of data or thing, which can be used to
+form assessments about its quality, reliability or
+trustworthiness. PROV-DM is the conceptual data model that forms a
+basis for the <abbr title="World Wide Web Consortium">W3C</abbr> provenance (PROV) family of specifications.
+</p>
+
+
+<p> This document presents a model-theoretic semantics for the PROV
+data model (called the <dfn id="dfn-reference-semantics">reference semantics</dfn>), viewing
+PROV-DM statements as atomic formulas in the sense of first-order
+logic, and viewing the constraints and inferences specified in
+PROV-CONSTRAINTS as a first-order theory. It is shown that the
+first-order theory is sound with respect to the reference semantics.
+This information may be useful to researchers or users of PROV to
+understand the intended meaning and use of PROV for modeling
+information about the actual history, derivation or evolution of Web
+resources. It may also be useful for development of additional
+constraints or inferences for reasoning about PROV or integration of
+PROV with other Semantic Web vocabularies. It is <b>not</b> proposed
+as a canonical or required semantics of PROV and does not place any
+constraints on use of PROV.</p>
+
+<p>The PROV Document Overview describes the overall state of PROV, and should be read before other PROV documents.</p>
+</section><section id="sotd" class="introductory"><h2>Status of This Document</h2>
+
+
+
+ <p>
+ <em>This section describes the status of this document at the time of its publication. Other
+ documents may supersede this document. A list of current <abbr title="World Wide Web Consortium">W3C</abbr> publications and the latest revision
+ of this technical report can be found in the <a href="http://www.w3.org/TR/"><abbr title="World Wide Web Consortium">W3C</abbr> technical reports
+ index</a> at http://www.w3.org/TR/.</em>
+ </p>
+
+<h4 id="prov-family-of-documents">PROV Family of Documents</h4>
+This document is part of the PROV family of documents, a set of documents defining various aspects that are necessary to achieve the vision of inter-operable
+interchange of provenance information in heterogeneous environments such as the Web. These documents are listed below. Please consult the [<cite><a href="#bib-PROV-OVERVIEW" class="bibref">PROV-OVERVIEW</a></cite>] for a guide to reading these documents.
+<ul>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">PROV-OVERVIEW</a> (To be published as Note), an overview of the PROV family of documents [<cite><a href="#bib-PROV-OVERVIEW" class="bibref">PROV-OVERVIEW</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">PROV-PRIMER</a> (To be published as Note), a primer for the PROV data model [<cite><a href="#bib-PROV-PRIMER" class="bibref">PROV-PRIMER</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">PROV-O</a> (Proposed Recommendation), the PROV ontology, an OWL2 ontology allowing the mapping of PROV to RDF [<cite><a href="#bib-PROV-O" class="bibref">PROV-O</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">PROV-DM</a> (Proposed Recommendation), the PROV data model for provenance [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">PROV-N</a> (Proposed Recommendation), a notation for provenance aimed at human consumption [<cite><a href="#bib-PROV-N" class="bibref">PROV-N</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">PROV-CONSTRAINTS</a> (Proposed Recommendation), a set of constraints applying to the PROV data model (this document);</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">PROV-XML</a> (To be published as Note), an XML schema for the PROV data model [<cite><a href="#bib-PROV-XML" class="bibref">PROV-XML</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">PROV-AQ</a> (To be published as Note), the mechanisms for accessing and querying provenance [<cite><a href="#bib-PROV-AQ" class="bibref">PROV-AQ</a></cite>]; </li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">PROV-DICTIONARY</a> (To be published as Note) introduces a specific type of collection, consisting of key-entity pairs [<cite><a href="#bib-PROV-DICTIONARY" class="bibref">PROV-DICTIONARY</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">PROV-DC</a> (To be published as Note) provides a mapping between PROV and Dublic Core Terms [<cite><a href="#bib-PROV-DC" class="bibref">PROV-DC</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312/">PROV-SEM</a> (To be published as Note), a declarative specification in terms of first-order logic of the PROV data model [<cite><a href="#bib-PROV-SEM" class="bibref">PROV-SEM</a></cite>];</li>
+<li> <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">PROV-LINKS</a> (To be published as Note) introduces a mechanism to link across bundles [<cite><a href="#bib-PROV-LINKS" class="bibref">PROV-LINKS</a></cite>].</li>
+</ul>
+
+
+ <p>
+ This document was published by the <a href="http://www.w3.org/2011/prov/">Provenance Working Group</a> as an Editor's Draft.
+
+
+ If you wish to make comments regarding this document, please send them to
+ <a href="mailto:public-prov-comments@w3.org">public-prov-comments@w3.org</a>
+ (<a href="mailto:public-prov-comments-request@w3.org?subject=subscribe">subscribe</a>,
+ <a href="http://lists.w3.org/Archives/Public/public-prov-comments/">archives</a>).
+
+
+
+
+ All comments are welcome.
+
+
+ </p><p>
+ Publication as an Editor's Draft does not imply endorsement by the <abbr title="World Wide Web Consortium">W3C</abbr> Membership.
+ This is a draft document and may be updated, replaced or obsoleted by other documents at
+ any time. It is inappropriate to cite this document as other than work in progress.
+ </p>
+
+
+ <p>
+
+ This document was produced by a group operating under the
+ <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
+
+
+
+
+ <abbr title="World Wide Web Consortium">W3C</abbr> maintains a <a href="http://www.w3.org/2004/01/pp-impl/46974/status" rel="disclosure">public list of any patent disclosures</a>
+
+ made in connection with the deliverables of the group; that page also includes instructions for
+ disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains
+ <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a> must disclose the
+ information in accordance with <a href="http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section
+ 6 of the <abbr title="World Wide Web Consortium">W3C</abbr> Patent Policy</a>.
+
+
+ </p>
+
+
+
+
+</section><section id="toc"><h2 class="introductory">Table of Contents</h2><ul class="toc"><li class="tocline"><a class="tocxref" href="#introduction"><span class="secno">1. </span>Introduction</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#purpose"><span class="secno">1.1 </span>Purpose of this document</a></li><li class="tocline"><a class="tocxref" href="#structure-of-this-document"><span class="secno">1.2 </span>Structure of this document</a></li><li class="tocline"><a class="tocxref" href="#audience"><span class="secno">1.3 </span> Audience </a></li></ul></li><li class="tocline"><a class="tocxref" href="#basics"><span class="secno">2. </span> Basics </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#identifiers"><span class="secno">2.1 </span> Identifiers </a></li><li class="tocline"><a class="tocxref" href="#times-and-intervals"><span class="secno">2.2 </span> Times and Intervals </a></li><li class="tocline"><a class="tocxref" href="#attributes-and-values"><span class="secno">2.3 </span> Attributes and Values </a></li><li class="tocline"><a class="tocxref" href="#formulas"><span class="secno">2.4 </span>Atomic Formulas</a></li><li class="tocline"><a class="tocxref" href="#first-order-formulas"><span class="secno">2.5 </span>First-Order Formulas</a></li></ul></li><li class="tocline"><a class="tocxref" href="#structures"><span class="secno">3. </span> Structures and Interpretations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#things-1"><span class="secno">3.1 </span> Things </a></li><li class="tocline"><a class="tocxref" href="#objects-1"><span class="secno">3.2 </span> Objects </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#entities-1"><span class="secno">3.2.1 </span> Entities </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#plans-1"><span class="secno">3.2.1.1 </span> Plans </a></li></ul></li><li class="tocline"><a class="tocxref" href="#actvities"><span class="secno">3.2.2 </span> Actvities </a></li><li class="tocline"><a class="tocxref" href="#agents-1"><span class="secno">3.2.3 </span> Agents </a></li><li class="tocline"><a class="tocxref" href="#interactions-1"><span class="secno">3.2.4 </span> Interactions </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#events-1"><span class="secno">3.2.4.1 </span> Events </a></li><li class="tocline"><a class="tocxref" href="#associations-1"><span class="secno">3.2.4.2 </span> Associations </a></li><li class="tocline"><a class="tocxref" href="#communications"><span class="secno">3.2.4.3 </span>Communications</a></li><li class="tocline"><a class="tocxref" href="#delegations"><span class="secno">3.2.4.4 </span>Delegations</a></li><li class="tocline"><a class="tocxref" href="#derivations-1"><span class="secno">3.2.4.5 </span> Derivations </a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#relations"><span class="secno">3.3 </span> Relations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#derivation-paths-and-derivedfrom"><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </a></li></ul></li><li class="tocline"><a class="tocxref" href="#putting-it-all-together"><span class="secno">3.4 </span> Putting it all together </a></li><li class="tocline"><a class="tocxref" href="#interpretations"><span class="secno">3.5 </span> Interpretations </a></li></ul></li><li class="tocline"><a class="tocxref" href="#semantics"><span class="secno">4. </span> Semantics </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#satisfaction"><span class="secno">4.1 </span> Satisfaction </a></li><li class="tocline"><a class="tocxref" href="#attribute-matching"><span class="secno">4.2 </span> Attribute matching </a></li><li class="tocline"><a class="tocxref" href="#semantics-of-element-formulas"><span class="secno">4.3 </span> Semantics of Element Formulas </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#entity"><span class="secno">4.3.1 </span> Entity </a></li><li class="tocline"><a class="tocxref" href="#activity"><span class="secno">4.3.2 </span> Activity </a></li><li class="tocline"><a class="tocxref" href="#agent"><span class="secno">4.3.3 </span> Agent </a></li></ul></li><li class="tocline"><a class="tocxref" href="#semantics-of-relations"><span class="secno">4.4 </span> Semantics of Relations </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#generation"><span class="secno">4.4.1 </span> Generation </a></li><li class="tocline"><a class="tocxref" href="#use"><span class="secno">4.4.2 </span> Use </a></li><li class="tocline"><a class="tocxref" href="#invalidation"><span class="secno">4.4.3 </span> Invalidation </a></li><li class="tocline"><a class="tocxref" href="#association"><span class="secno">4.4.4 </span> Association </a></li><li class="tocline"><a class="tocxref" href="#start-formulas"><span class="secno">4.4.5 </span> Start Formulas </a></li><li class="tocline"><a class="tocxref" href="#end"><span class="secno">4.4.6 </span> End </a></li><li class="tocline"><a class="tocxref" href="#attribution"><span class="secno">4.4.7 </span> Attribution </a></li><li class="tocline"><a class="tocxref" href="#communication"><span class="secno">4.4.8 </span>Communication</a></li><li class="tocline"><a class="tocxref" href="#responsibility"><span class="secno">4.4.9 </span> Responsibility </a></li><li class="tocline"><a class="tocxref" href="#derivation"><span class="secno">4.4.10 </span> Derivation </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#precise"><span class="secno">4.4.10.1 </span> Precise </a></li><li class="tocline"><a class="tocxref" href="#imprecise"><span class="secno">4.4.10.2 </span> Imprecise </a></li></ul></li><li class="tocline"><a class="tocxref" href="#influence"><span class="secno">4.4.11 </span>Influence</a></li><li class="tocline"><a class="tocxref" href="#specialization"><span class="secno">4.4.12 </span> Specialization </a></li><li class="tocline"><a class="tocxref" href="#alternate"><span class="secno">4.4.13 </span> Alternate </a></li><li class="tocline"><a class="tocxref" href="#membership"><span class="secno">4.4.14 </span> Membership </a></li></ul></li><li class="tocline"><a class="tocxref" href="#auxiliary-formulas"><span class="secno">4.5 </span>Auxiliary formulas</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#equals"><span class="secno">4.5.1 </span>Equals</a></li><li class="tocline"><a class="tocxref" href="#precedes-and-strictly-precedes"><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</a></li><li class="tocline"><a class="tocxref" href="#notnull"><span class="secno">4.5.3 </span>notNull</a></li><li class="tocline"><a class="tocxref" href="#typeof"><span class="secno">4.5.4 </span>typeOf</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#theory"><span class="secno">5. </span> Inferences and Constraints </a><ul class="toc"><li class="tocline"><a class="tocxref" href="#inferences"><span class="secno">5.1 </span>Inferences</a></li><li class="tocline"><a class="tocxref" href="#constraints"><span class="secno">5.2 </span>Constraints</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#uniqueness-constraints"><span class="secno">5.2.1 </span>Uniqueness constraints</a></li><li class="tocline"><a class="tocxref" href="#ordering-constraints"><span class="secno">5.2.2 </span>Ordering constraints</a></li><li class="tocline"><a class="tocxref" href="#typing-constraints"><span class="secno">5.2.3 </span>Typing constraints</a></li><li class="tocline"><a class="tocxref" href="#impossibility-constraints"><span class="secno">5.2.4 </span>Impossibility constraints</a></li></ul></li></ul></li><li class="tocline"><a class="tocxref" href="#soundness"><span class="secno">6. </span>Soundness</a></li><li class="tocline"><a class="tocxref" href="#acknowledgements"><span class="secno">A. </span>Acknowledgements</a></li><li class="tocline"><a class="tocxref" href="#references"><span class="secno">B. </span>References</a><ul class="toc"><li class="tocline"><a class="tocxref" href="#informative-references"><span class="secno">B.1 </span>Informative references</a></li></ul></li></ul></section>
+
+
+
+
+
+
+ <section id="introduction">
+ <!--OddPage--><h2><span class="secno">1. </span>Introduction</h2>
+
+<p>
+Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing.
+This document complements
+ the PROV-DM specification [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>] that defines a data model for
+ provenance on the Web, and the PROV-CONSTRAINTS specification
+[<cite><a href="#bib-PROV-CONSTRAINTS" class="bibref">PROV-CONSTRAINTS</a></cite>] that
+specifies definitions, inferences, and constraints that can be used to
+reason about PROV documents, or determine their validity. This document
+provides a reference formal semantics of PROV, providing a formal
+counterpart to the informal descriptions and motivations given
+elsewhere in PROV specifications.</p>
+
+
+
+<!--
+<section id="conventions">
+<h3>Conventions</h3>
+
+
+<p>In this document, logical formulas contain variables written as
+ lower-case identifiers. Some of these variables are written
+ beginning with the underscore character <span
+ class="name">_</span>, by convention, to indicate that they
+ appear only once in the formula. Such variables are
+ provided merely as an aid to the reader. </p>
+
+</section>
+-->
+
+<section id="purpose">
+
+<h3><span class="secno">1.1 </span>Purpose of this document</h3>
+
+</section>
+<p>The PROV-DM and PROV-CONSTRAINTS give motivating examples that
+provide an intuition about the meaning of the constructs. For some
+concepts, such as use, start, end, generation/invalidation, and
+derivation, the meaning is either obvious or situation-dependent.
+However, during the development of PROV, the importance of additional
+concepts became evident, but the intuitive meaning or correct use of
+these concepts were not clear. For example, the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-1-Frame" class="MathJax"><nobr><span id="MathJax-Span-1" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-1" type="math/tex">alternateOf</script> and
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-2-Frame" class="MathJax"><nobr><span id="MathJax-Span-14" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-22" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-23" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-24" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-25" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-26" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-27" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-28" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-29" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-30" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-31" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-2" type="math/tex">specializationOf</script> relations are used in PROV to relate different
+entities that present aspects of "the same thing".
+Over time the working group came to a
+consensus about these concepts and how they are to be used, but this
+understanding is based on abstract notions that are not explicit in
+PROV documents; instead, some of their properties are captured
+formally through certain constraints and inferences, while others are
+not captured in PROV specifications at all.
+</p>
+
+<p>The purpose of this document is to present the working group's
+consensus view of the semantics of PROV, using tools from mathematical
+logic, principally model theory (though our use of these tools is lightweight). This information may be useful to users for understanding the
+intent behind certain features of PROV, to researchers investigating
+richer forms of reasoning over provenance, or to future efforts
+building upon PROV. It is intended as an exploration of a <b>reference</b>
+semantics for PROV, not a definitive specification of the <b>only</b>
+semantics of PROV. </p>
+
+<p> Nevertheless, the reference semantics does have appealing
+properties. Specifically, it provides a declarative counterpart to
+the operational definition of validity taken in PROV-CONSTRAINTS. In
+the specification, validity is defined via a normalization process
+followed by constraint checking on the normal form. This approach was adopted
+to keep the specification closer to implementations, although other
+implementations are possible and allowed. In addition to providing a
+reference semantics, this document shows that the operational
+presentation of PROV validity checking is sound with respect to
+declarative presentation adopted here. This could help justify
+alternative approaches to validity checking.</p>
+
+<section id="structure-of-this-document"> <h3><span class="secno">1.2 </span>Structure of this document</h3> <p>
+
+</p>
+
+<ul>
+ <li><a href="#basics">Section 2</a> summarizes the basic concepts
+ from mathematical logic used in the semantics, recapitulates how
+ PROV statements can be viewed as atomic formulas, and introduces
+ some auxiliary formulas.</li>
+ <li><a href="#structures">Section 3</a> presents the mathematical
+ structures used for situations that PROV statements can
+ describe.</li>
+ <li><a href="#semantics">Section 4</a> defines the semantics of PROV
+ statements and auxiliary formulas, indicating when a given formula
+ is satisfied in a structure.</li>
+ <li><a href="#theory">Section 5</a> presents the inferences and
+ constraints from PROV-CONSTRAINTS as first-order formulas, and gives
+ brief justifications for their soundness.</li>
+ <li><a href="#soundness">Section 6</a> relates the PROV notion of
+ validity to the logical notion of consistency. A PROV instance is
+ valid if and only if its corresponding first-order theory is
+ satisfiable.</li>
+</ul>
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ Completeness direction above doesn't hold for current semantics,
+ because attributes assumed to be single-valued; for
+ example, <span class="MathJax_Preview">entity(id,[a=1,a=2])</span><script id="MathJax-Element-3" type="math/tex">entity(id,[a=1,a=2])</script> is valid but doesn't have a
+ reference model.
+ </div></div>
+
+</section>
+<section id="audience">
+<h3><span class="secno">1.3 </span> Audience </h3>
+
+
+<p>This document assumes familiarity with [<cite><a href="#bib-PROV-DM" class="bibref">PROV-DM</a></cite>] and
+ [<cite><a href="#bib-PROV-CONSTRAINTS" class="bibref">PROV-CONSTRAINTS</a></cite>] and employs (a
+ simplified form of)
+[<cite><a href="#bib-PROV-N" class="bibref">PROV-N</a></cite>] notation. In particular it assumes familiarity with the concepts
+ from logic, and the relationship between PROV statements and
+ instances and first-order formulas and theories, respectively,
+ presented in <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/#overview">Section 2.5</a> of PROV-CONSTRAINTS.
+</p>
+
+ <p>This document may be useful to users of PROV who have a formal
+ background and are interested in the rationale for some of the
+ constructs of PROV; for resaerchers investigating extensions of PROV
+ or alternative approaches to reasoning about PROV; or for future
+ efforts on provenance standardization. </p>
+
+ </section>
+
+ </section>
+
+
+ <!--
+
+<section id="overview">
+<h2> Overview </h2>
+
+
+<p>The idea of this document is to sketch what aspects of the provenance model can be formalized and how they can be formalized, as a first step towards establishing a consensus on the (intended) meaning of the components of the model and the consistency constraints or inferences that can be applied to the model to distinguish valid from invalid provenance records.</p>
+
+<p>The <a href="http://www.w3.org/TR/prov-constraints/">PROV-CONSTRAINTS</a> document contains formal content specifying a notion of validity (approximately, logical consistency) for PROV documents. The formal semantics, PROV-SEM, is planned for release as a W3C Note that will complement the procedural specification in PROV-CONSTRAINTS with a declarative specification formulated in terms of first-order logic. The formal semantics is <b>work in progress</b>. The drafts below are intermediate stages and some of them are out of date.
+</p>
+
+<h3> Status </h3>
+
+<p>
+This is work in progress. The semantics is being updated to be consistent with the Candidate Recommendation of PROV. The plan is to release the semantics as a Note over the next few months. At that point, the wiki pages containing drafts of the semantics will be superseded.
+</p>
+
+
+<h3> Idea of the semantics </h3>
+
+<p>As a starting point, I will assume that we intend the statements made in a PROV-DM instance to be intended to describe one, consistent state of the world, much like a logical formula is said to be satisfied in a mathematical model. That is, I propose an approach similar to that taken in model theory, where the PROV-DM instance corresponds to a formula or theory of a logic, and the semantics corresponds to what logicians call a model.</p>
+
+<p>For example, the formula $\forall x. P(x) \Rightarrow Q(x)$ is satisfied in a mathematical model where the relation $P$ denotes a set of elements that is contained in that denoted by $Q$. Here, the goal is to come up with a plausible "intended model" for interpreting PROV-DM instances, where the formulas are statements in PROV-DM and the individuals are things and agents. This is complicated by the fact that many statements about provenance involve talking about objects that change over time.</p>
+
+<p>The word "world" is used in PROV-DM to talk about the actual state
+of affairs that the PROV-DM instance describes, which is what I would
+usually call a "model". The word "model" is used in PROV-DM mainly in
+the sense of "data model", that is, to talk about what I would
+otherwise call the syntax of PROV-DM. To avoid confusion with the
+uses of terms in PROV-DM, I will use "structure" to describe the
+mathematical structure that corresponds to actual state of affairs.
+We use the term "model" to describe a structure that satisfies a given
+theory; this sense of "model" does not mean "data model".</p>
+
+<h3> Axiomatization and relationship to PROV-CONSTRAINTS </h3>
+
+<p>One goal of the semantics is to link the procedural specification of validity and equivalence with traditional notions of logical consistency and equivalence of theories, for example in first-order logic. A first-order axiomatization that corresponds to the formal constraints and is sound for reasoning about the models described below is in progress at the end of the document.
+</p>
+</section>
+-->
+
+<section id="basics">
+<!--OddPage--><h2><span class="secno">2. </span> Basics </h2>
+
+
+
+
+
+<section id="identifiers">
+<h3><span class="secno">2.1 </span> Identifiers </h3>
+
+<p>A lowercase symbol <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-4-Frame" class="MathJax"><nobr><span id="MathJax-Span-54" class="math"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-55" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-56" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-57" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-58" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-59" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-60" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-61" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-62" class="mo">.</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-4" type="math/tex">x,y,...</script> on its own denotes an identifier.
+Identifiers may or may not be URIs. Identifiers are viewed as variables in logic (or blank nodes in RDF): just because we have two different identifiers <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-5-Frame" class="MathJax"><nobr><span id="MathJax-Span-63" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-64" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-65" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-5" type="math/tex">x</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-6-Frame" class="MathJax"><nobr><span id="MathJax-Span-66" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.55em); top: -2.57em; left: 0em;"><span id="MathJax-Span-67" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-68" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-6" type="math/tex">y</script> doesn't tell us that they denote different things, since we could discover that they are actually the same later. We write <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-7-Frame" class="MathJax"><nobr><span id="MathJax-Span-69" class="math"><span style="display: inline-block; position: relative; width: 75px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-70" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-71" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-72" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-73" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-74" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-75" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-76" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-77" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-78" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-79" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-80" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-81" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-7" type="math/tex">Identifiers</script> for the set of identifiers of interest in a given situation (typically, the set of identifiers present in the PROV instance of interest).
+</p>
+</section>
+
+<section id="times-and-intervals">
+<h3><span class="secno">2.2 </span> Times and Intervals </h3>
+
+<p>We assume a linearly ordered set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-8-Frame" class="MathJax"><nobr><span id="MathJax-Span-82" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-83" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-84" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-85" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-86" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-87" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-88" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-89" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-90" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-91" class="mo">≤</span><span style="font-family: STIXGeneral;" id="MathJax-Span-92" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-8" type="math/tex">(Times,\leq)</script> of time instants. For convenience we assume the order is total or linear order, corresponding to a linear timeline; however, PROV does not assume that time is linear and events could be partially ordered and not necessarily reconciled to a single global clock.
+</p>
+<p>We also consider a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-9-Frame" class="MathJax"><nobr><span id="MathJax-Span-93" class="math"><span style="display: inline-block; position: relative; width: 62px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-94" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-95" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-96" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-97" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-98" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-99" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-100" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-101" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-102" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-103" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-9" type="math/tex">Intervals</script> of closed intervals of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-10-Frame" class="MathJax"><nobr><span id="MathJax-Span-104" class="math"><span style="display: inline-block; position: relative; width: 108px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.705em, 1000em, 2.934em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-105" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-106" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-108" class="mo">∣</span><span style="padding-left: 0.313em;" id="MathJax-Span-109" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-111" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-112" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-113" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-114" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-115" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-117" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-118" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.066em; vertical-align: -0.265em;"></span></span></nobr></span><script id="MathJax-Element-10" type="math/tex">\{t \mid t_1 \leq t \leq t_2\}</script>.
+</p>
+</section>
+
+<section id="attributes-and-values">
+<h3><span class="secno">2.3 </span> Attributes and Values </h3>
+
+<p>We assume a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-11-Frame" class="MathJax"><nobr><span id="MathJax-Span-119" class="math"><span style="display: inline-block; position: relative; width: 69px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-120" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-121" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-122" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-123" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-124" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-125" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-126" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-127" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-129" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-130" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-11" type="math/tex">Attributes</script> of attribute labels and a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-12-Frame" class="MathJax"><nobr><span id="MathJax-Span-131" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.45em); top: -2.57em; left: 0em;"><span id="MathJax-Span-132" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-133" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-134" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-135" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-136" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-137" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-138" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-12" type="math/tex">Values</script>
+of possible values of attributes. To allow for the fact that some
+attributes can have undefined or multiple values, we sometimes use the set
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-13-Frame" class="MathJax"><nobr><span id="MathJax-Span-139" class="math"><span style="display: inline-block; position: relative; width: 63px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-141" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-142" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-143" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-144" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-145" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-146" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-147" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-148" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-13" type="math/tex">P(Value)</script>, that is, the set of sets of values.
+</p> </section>
+
+<section id="formulas">
+<h3><span class="secno">2.4 </span>Atomic Formulas</h3>
+
+<p>The following atomic formulas correspond to the statements of PROV-DM. We assume that definitions 1-4 of PROV-CONSTRAINTS have been applied in order to expand all optional parameters; thus, we use uniform notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-14-Frame" class="MathJax"><nobr><span id="MathJax-Span-149" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-150" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-151" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-152" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-153" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-154" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-155" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-157" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-158" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-159" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-160" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-161" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-162" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-163" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-164" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-165" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-14" type="math/tex">r(id,a_1,\ldots,a_n)</script> instead of the semicolon notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-15-Frame" class="MathJax"><nobr><span id="MathJax-Span-166" class="math"><span style="display: inline-block; position: relative; width: 107px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-168" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-169" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-170" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-171" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-172" class="mo">;</span><span style="padding-left: 0.188em;" id="MathJax-Span-173" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-174" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-175" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-176" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-177" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-178" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-179" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-180" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-181" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-182" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-15" type="math/tex">r(id;a_1,\ldots,a_n)</script>.
+</p>
+<p>Each parameter is either an identifier, a constant (e.g. a time or other literal value in an attribute list), or a null symbol "-". Null symbols can only appear in the specified arguments in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-16-Frame" class="MathJax"><nobr><span id="MathJax-Span-183" class="math"><span style="display: inline-block; position: relative; width: 135px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-184" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-185" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-187" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-188" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-189" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-190" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-191" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-192" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-193" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-194" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-196" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-197" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-198" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-199" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-200" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-201" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-16" type="math/tex">wasAssociatedWith</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-17-Frame" class="MathJax"><nobr><span id="MathJax-Span-202" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-203" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-204" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-206" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-207" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-208" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-209" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-210" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-211" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-212" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-213" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-214" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-215" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-216" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-217" class="mi">m</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-17" type="math/tex">wasDerivedFrom</script>, as shown in the grammar below.
+</p>
+<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-18-Frame" class="MathJax"><nobr><span id="MathJax-Span-218" class="math"><span style="display: inline-block; position: relative; width: 487px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(-20.206em, 1000em, 23.795em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-219" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-220" class="mtable"><span style="display: inline-block; position: relative; width: 28.126em; height: 0px;"><span style="position: absolute; clip: rect(22.201em, 1000em, 65.879em, -0.526em); top: -44.334em; left: 0em;"><span style="display: inline-block; position: relative; width: 7.477em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -23.845em; right: 0em;"><span id="MathJax-Span-221" class="mtd"><span id="MathJax-Span-222" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-223" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-224" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-225" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-226" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-227" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-228" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-229" class="mi">_</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-230" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-231" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-232" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-233" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-234" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-235" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-236" class="mi">a</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -23.907em; right: 0em;"><span id="MathJax-Span-259" class="mtd"><span id="MathJax-Span-260" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -22.567em; right: 0em;"><span id="MathJax-Span-284" class="mtd"><span id="MathJax-Span-285" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.495em); top: -19.825em; right: 0em;"><span id="MathJax-Span-310" class="mtd"><span id="MathJax-Span-311" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-312" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-313" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-315" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-316" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-317" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-318" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-319" class="mi">_</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-320" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-321" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-322" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-323" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-324" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-325" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-326" class="mi">a</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -19.887em; right: 0em;"><span id="MathJax-Span-350" class="mtd"><span id="MathJax-Span-351" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -18.548em; right: 0em;"><span id="MathJax-Span-383" class="mtd"><span id="MathJax-Span-384" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.481em); top: -15.807em; right: 0em;"><span id="MathJax-Span-407" class="mtd"><span id="MathJax-Span-408" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-409" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-410" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-411" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-412" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-414" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-415" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-416" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-417" class="mi">_</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-418" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-419" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-420" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-421" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-422" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-423" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-424" class="mi">a</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -15.869em; right: 0em;"><span id="MathJax-Span-462" class="mtd"><span id="MathJax-Span-463" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -14.559em; right: 0em;"><span id="MathJax-Span-491" class="mtd"><span id="MathJax-Span-492" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -13.22em; right: 0em;"><span id="MathJax-Span-532" class="mtd"><span id="MathJax-Span-533" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -11.881em; right: 0em;"><span id="MathJax-Span-573" class="mtd"><span id="MathJax-Span-574" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -10.542em; right: 0em;"><span id="MathJax-Span-612" class="mtd"><span id="MathJax-Span-613" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -9.203em; right: 0em;"><span id="MathJax-Span-658" class="mtd"><span id="MathJax-Span-659" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -7.864em; right: 0em;"><span id="MathJax-Span-703" class="mtd"><span id="MathJax-Span-704" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -6.525em; right: 0em;"><span id="MathJax-Span-742" class="mtd"><span id="MathJax-Span-743" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -5.151em; right: 0em;"><span id="MathJax-Span-790" class="mtd"><span id="MathJax-Span-791" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -3.811em; right: 0em;"><span id="MathJax-Span-830" class="mtd"><span id="MathJax-Span-831" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -2.472em; right: 0em;"><span id="MathJax-Span-879" class="mtd"><span id="MathJax-Span-880" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -1.162em; right: 0em;"><span id="MathJax-Span-926" class="mtd"><span id="MathJax-Span-927" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 0.178em; right: 0em;"><span id="MathJax-Span-964" class="mtd"><span id="MathJax-Span-965" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 1.518em; right: 0em;"><span id="MathJax-Span-993" class="mtd"><span id="MathJax-Span-994" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 2.858em; right: 0em;"><span id="MathJax-Span-1027" class="mtd"><span id="MathJax-Span-1028" class="mrow"></span></span><span style="display: inline-block; 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height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -19.825em; left: 0em;"><span id="MathJax-Span-332" class="mtd"><span id="MathJax-Span-333" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-334" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-335" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-337" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-338" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-339" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-340" class="mo">(</span><span style="font-family: STIXGeneral; 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top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1178" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1179" class="mo">]</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.495em); top: 13.458em; left: 0em;"><span id="MathJax-Span-1189" class="mtd"><span id="MathJax-Span-1190" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1192" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1194" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1196" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.509em); top: 14.79em; left: 0em;"><span id="MathJax-Span-1204" class="mtd"><span id="MathJax-Span-1205" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1207" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1209" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1210" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1211" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1213" class="mi">y</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: 16.122em; left: 0em;"><span id="MathJax-Span-1221" class="mtd"><span id="MathJax-Span-1222" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1223" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1224" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1225" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1226" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: 17.461em; left: 0em;"><span id="MathJax-Span-1235" class="mtd"><span id="MathJax-Span-1236" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1237" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1238" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1239" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1240" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1241" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1242" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1243" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1245" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1246" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1247" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1250" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1251" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.601em); top: 18.799em; left: 0em;"><span id="MathJax-Span-1259" class="mtd"><span id="MathJax-Span-1260" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1261" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1262" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1263" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1264" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1265" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1266" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1267" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1268" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1269" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1270" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1271" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1272" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1273" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1274" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1276" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1277" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1278" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1279" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1280" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 44.509em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 46.831em; vertical-align: -23.148em;"></span></span></nobr></span></div><script id="MathJax-Element-18" type="math/tex; mode=display">
+\begin{array}{rcl}
+ atomic\_formula & {::=}& element\_formula\\
+ & | & relation\_formula\\
+ & | & auxiliary\_formula\\
+ element\_formula
+ &{::=} &entity(id,attrs) \\
+ & |& activity(id,st,et,attrs)\\
+ & |& agent(id,attrs)\\
+ relation\_formula
+ &{::=}& wasGeneratedBy(id,e,a,t,attrs)\\
+ & |& used(id,e,a,t,attrs)\\
+ & |& wasInvalidatedBy(id,e,a,t,attrs)\\
+ & |& wasStartedBy(id,a_2,e,a_1,attrs)\\
+ & |& wasEndedBy(id,a_2,e,a_1,attrs)\\
+ & |& wasAssociatedWith(id,ag,act,pl,attrs)\\
+ & |& wasAssociatedWith(id,ag,act,-,attrs)\\
+ & |& wasAttributedTo(id,e,ag,attrs)\\
+ & |& actedOnBehalfOf(if,ag_2,ag_1,act,attrs)\\
+ & |& wasInformedBy(id,a_2,a_1,attrs)\\
+ & |& wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)\\
+ & |& wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)\\
+& | & wasInfluencedBy(id,x,y,attrs)\\
+ & |& alternateOf(e_1,e_2)\\
+ & |& specializationOf(e_1,e_2)\\
+ & | & hadMember(c,e)\\
+ auxiliary\_formula
+ &{::=}& x = y\\
+ & | & x \prec y\\
+ & | & x \preceq y\\
+ & | & notNull(x)\\
+ & | & typeOf(x,ty)\\
+attrs &::=& [attr_1 = v_1, \ldots,attr_n = v_n]\\
+ ty &{::=}& entity \\
+&|& activity\\
+&|& agent\\
+&|& prov:Collection\\
+&|& prov:EmptyCollection
+\end{array}
+</script>
+
+</section>
+
+<section id="first-order-formulas">
+<h3><span class="secno">2.5 </span>First-Order Formulas</h3>
+
+<p>We also consider the usual connectives and quantifiers of
+first-order logic [<cite><a href="#bib-Logic" class="bibref">Logic</a></cite>].
+<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-19-Frame" class="MathJax"><nobr><span id="MathJax-Span-1281" class="math"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(-4.148em, 1000em, 7.737em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-1282" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-1283" class="mtable"><span style="display: inline-block; position: relative; width: 10.778em; height: 0px;"><span style="position: absolute; clip: rect(6.133em, 1000em, 17.695em, -0.526em); top: -12.208em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.643em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -7.787em; right: 0em;"><span id="MathJax-Span-1284" class="mtd"><span id="MathJax-Span-1285" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1286" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -7.856em; right: 0em;"><span id="MathJax-Span-1308" class="mtd"><span id="MathJax-Span-1309" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -6.656em; right: 0em;"><span id="MathJax-Span-1321" class="mtd"><span id="MathJax-Span-1322" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -5.456em; right: 0em;"><span id="MathJax-Span-1335" class="mtd"><span id="MathJax-Span-1336" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -4.118em; right: 0em;"><span id="MathJax-Span-1347" class="mtd"><span id="MathJax-Span-1348" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -2.745em; right: 0em;"><span id="MathJax-Span-1363" class="mtd"><span id="MathJax-Span-1364" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: -1.371em; right: 0em;"><span id="MathJax-Span-1379" class="mtd"><span id="MathJax-Span-1380" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 0.002em; right: 0em;"><span id="MathJax-Span-1395" class="mtd"><span id="MathJax-Span-1396" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span><span style="position: absolute; clip: rect(3.797em, 1000em, 4.147em, -0.526em); top: 1.34em; right: 0em;"><span id="MathJax-Span-1408" class="mtd"><span id="MathJax-Span-1409" class="mrow"></span></span><span style="display: inline-block; width: 0px; height: 3.972em;"></span></span></span><span style="display: inline-block; width: 0px; height: 12.208em;"></span></span><span style="position: absolute; clip: rect(6.123em, 1000em, 17.476em, -0.459em); top: -11.974em; left: 1.768em;"><span style="display: inline-block; position: relative; width: 1.285em; height: 0px;"><span style="position: absolute; clip: rect(1.936em, 1000em, 2.756em, -0.445em); top: -7.787em; left: 50%; margin-left: -0.643em;"><span id="MathJax-Span-1287" class="mtd"><span id="MathJax-Span-1288" class="mrow"><span id="MathJax-Span-1289" class="texatom"><span id="MathJax-Span-1290" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1291" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">:</span><span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -6.454em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1310" class="mtd"><span id="MathJax-Span-1311" class="mrow"><span id="MathJax-Span-1312" class="texatom"><span id="MathJax-Span-1313" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1314" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -5.254em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1323" class="mtd"><span id="MathJax-Span-1324" class="mrow"><span id="MathJax-Span-1325" class="texatom"><span id="MathJax-Span-1326" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1327" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -4.054em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1337" class="mtd"><span id="MathJax-Span-1338" class="mrow"><span id="MathJax-Span-1339" class="texatom"><span id="MathJax-Span-1340" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1341" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -2.716em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1349" class="mtd"><span id="MathJax-Span-1350" class="mrow"><span id="MathJax-Span-1351" class="texatom"><span id="MathJax-Span-1352" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1353" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: -1.343em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1365" class="mtd"><span id="MathJax-Span-1366" class="mrow"><span id="MathJax-Span-1367" class="texatom"><span id="MathJax-Span-1368" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1369" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 0.031em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1381" class="mtd"><span id="MathJax-Span-1382" class="mrow"><span id="MathJax-Span-1383" class="texatom"><span id="MathJax-Span-1384" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1385" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 1.404em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1397" class="mtd"><span id="MathJax-Span-1398" class="mrow"><span id="MathJax-Span-1399" class="texatom"><span id="MathJax-Span-1400" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1401" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.759em, -0.459em); top: 2.742em; left: 50%; margin-left: -0.146em;"><span id="MathJax-Span-1410" class="mtd"><span id="MathJax-Span-1411" class="mrow"><span id="MathJax-Span-1412" class="texatom"><span id="MathJax-Span-1413" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1414" class="mo">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 11.974em;"></span></span><span style="position: absolute; clip: rect(6.366em, 1000em, 18.134em, -0.524em); top: -12.442em; left: 4.178em;"><span style="display: inline-block; position: relative; width: 6.6em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -7.787em; left: 0em;"><span id="MathJax-Span-1292" class="mtd"><span id="MathJax-Span-1293" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1296" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1297" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1298" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1299" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1300" class="mi">_</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1301" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1303" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1304" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1305" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1306" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1307" class="mi">a</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.742em, 1000em, 2.756em, -0.467em); top: -6.454em; left: 0em;"><span id="MathJax-Span-1315" class="mtd"><span id="MathJax-Span-1316" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1317" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1318" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1319" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1320" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.518em); top: -5.254em; left: 0em;"><span id="MathJax-Span-1328" class="mtd"><span id="MathJax-Span-1329" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1330" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1331" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1332" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1333" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1334" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.478em); top: -4.054em; left: 0em;"><span id="MathJax-Span-1342" class="mtd"><span id="MathJax-Span-1343" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1344" class="mi">¬</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1345" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1346" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: -2.716em; left: 0em;"><span id="MathJax-Span-1354" class="mtd"><span id="MathJax-Span-1355" class="mrow"><span id="MathJax-Span-1356" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1357" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1358" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1359" class="mo">∧</span><span style="padding-left: 0.25em;" id="MathJax-Span-1360" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1361" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1362" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: -1.343em; left: 0em;"><span id="MathJax-Span-1370" class="mtd"><span id="MathJax-Span-1371" class="mrow"><span id="MathJax-Span-1372" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1373" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1374" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1375" class="mo">∨</span><span style="padding-left: 0.25em;" id="MathJax-Span-1376" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1377" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1378" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.986em, -0.499em); top: 0.031em; left: 0em;"><span id="MathJax-Span-1386" class="mtd"><span id="MathJax-Span-1387" class="mrow"><span id="MathJax-Span-1388" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1389" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1390" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1391" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-1392" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1393" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-1394" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.524em); top: 1.404em; left: 0em;"><span id="MathJax-Span-1402" class="mtd"><span id="MathJax-Span-1403" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1404" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1405" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1406" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1407" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.453em); top: 2.742em; left: 0em;"><span id="MathJax-Span-1415" class="mtd"><span id="MathJax-Span-1416" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1417" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1418" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1419" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1420" class="mi">ϕ</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 12.442em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 12.466em; vertical-align: -5.966em;"></span></span></nobr></span></div><script id="MathJax-Element-19" type="math/tex; mode=display">
+\begin{array}{rcl}
+ \phi &{::=}& atomic\_formula\\
+& | & True\\
+& | & False\\
+&|& \neg~\phi\\
+ &|& \phi_1 \wedge \phi_2\\
+ &|& \phi_1 \vee \phi_2\\
+ &|& \phi_1 \Rightarrow \phi_2\\
+&|& \forall x. \phi\\
+&|& \exists x. \phi\\
+\end{array}
+</script>
+
+
+</p></section>
+<!--
+<section>
+<h3>Instances as Theories</h3>
+<p>A PROV-DM
+instance can be viewed as a set of atomic formulas
+$\phi_1$...$\phi_n$, often called a <em>theory</em>. A theory is
+viewed as a conjunction, that is, the overall instance is considered
+to hold in a given structure if each atomic formula in it holds.</p>
+</section>
+-->
+
+
+</section>
+
+
+<section id="structures">
+<!--OddPage--><h2><span class="secno">3. </span> Structures and Interpretations </h2>
+
+<section id="things-1">
+
+<h3><span class="secno">3.1 </span> Things </h3>
+
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Containment of things / collections? (for hadMember).</div></div>
+<p><em>Things</em> are things in the world. Each thing has a lifetime during which it exists and attributes whose values can change over time.
+</p>
+<p>To model this, a structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-20-Frame" class="MathJax"><nobr><span id="MathJax-Span-1421" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1422" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1423" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-20" type="math/tex">W</script> includes:
+</p>
+<div data-title="Component 1 (things)" data-count="1" class="component" id="things"><div class="ruleTitle"><a href="#things" class="internalDFN">Component 1 (things)</a></div><ol>
+ <li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-21-Frame" class="MathJax"><nobr><span id="MathJax-Span-1424" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1425" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1426" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1427" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1428" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1429" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1430" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1431" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-21" type="math/tex">Things</script> of things</li>
+ <li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-22-Frame" class="MathJax"><nobr><span id="MathJax-Span-1432" class="math"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1433" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1434" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1435" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1436" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1437" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1438" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1439" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1440" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1441" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1442" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1443" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1444" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1445" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1446" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1447" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1448" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1449" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1450" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1451" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1452" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1453" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1454" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1455" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1456" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1457" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1458" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-22" type="math/tex">lifetime : Things \to Intervals</script> from objects to time intervals</li>
+ <li>a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-23-Frame" class="MathJax"><nobr><span id="MathJax-Span-1459" class="math"><span style="display: inline-block; position: relative; width: 349px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1460" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1461" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1462" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1463" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1464" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1465" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1466" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1467" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1468" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1469" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1470" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1471" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1472" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1473" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1474" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1476" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1477" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1478" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1479" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1480" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1481" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1483" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1484" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1485" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1486" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1487" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1488" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1489" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1490" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1491" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1492" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1493" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1494" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1495" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1496" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1497" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1498" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1499" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-23" type="math/tex">value : Things \times Attributes \times Times \to P(Values)</script>
+</li>
+</ol>
+</div>
+<p>
+The range of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-24-Frame" class="MathJax"><nobr><span id="MathJax-Span-1500" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1501" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1502" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1504" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1505" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1506" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-24" type="math/tex">value</script> is the set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-25-Frame" class="MathJax"><nobr><span id="MathJax-Span-1507" class="math"><span style="display: inline-block; position: relative; width: 70px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1508" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1509" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1510" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1511" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1512" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1513" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1514" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1515" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1516" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1517" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-25" type="math/tex">P(Values)</script>, indicating that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-26-Frame" class="MathJax"><nobr><span id="MathJax-Span-1518" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1519" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1520" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1521" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1522" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1523" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1524" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-26" type="math/tex">value</script>
+is essentially a multi-valued that returns a set of values (possibly empty). When <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-27-Frame" class="MathJax"><nobr><span id="MathJax-Span-1525" class="math"><span style="display: inline-block; position: relative; width: 116px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1526" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1527" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1528" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1529" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1530" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1531" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1532" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1533" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1534" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1535" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1538" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1539" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1540" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-27" type="math/tex">value(x,a,t) =
+\emptyset</script>, we say that attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-28-Frame" class="MathJax"><nobr><span id="MathJax-Span-1541" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1542" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1543" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-28" type="math/tex">a</script> is undefined for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-29-Frame" class="MathJax"><nobr><span id="MathJax-Span-1544" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1545" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1546" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-29" type="math/tex">x</script> at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-30-Frame" class="MathJax"><nobr><span id="MathJax-Span-1547" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1548" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-30" type="math/tex">t</script>.</p>
+
+<p>Note that this description does not say what the structure of a
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-31-Frame" class="MathJax"><nobr><span id="MathJax-Span-1550" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1551" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1552" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1553" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1554" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1555" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1556" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-31" type="math/tex">Thing</script> is, only how it may be described in terms of its time interval
+and attribute values. An object could just be a record of fixed
+attribute values; it could be a bear; it could be the Royal Society;
+it could be a transcendental number like <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-32-Frame" class="MathJax"><nobr><span id="MathJax-Span-1557" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.967em, 1000em, 2.763em, -0.507em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1558" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1559" class="mi">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.032em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.602em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-32" type="math/tex">\pi</script>. All that matters from
+our point of view is that we know how to map the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-33-Frame" class="MathJax"><nobr><span id="MathJax-Span-1560" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1561" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1562" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1563" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1565" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1566" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-33" type="math/tex">Thing</script> to its time interval and attribute mapping.
+</p>
+
+
+<p>It is possible for two Things to be indistinguishable by their attribute values and lifetime, but have different identity.
+</p>
+
+
+</section>
+
+<section id="objects-1">
+<h3><span class="secno">3.2 </span> Objects </h3>
+
+<p>
+An <em>Object</em> is described by a time interval and attributes with unchanging values. Objects encompass entities, interactions, and activities.
+To model this, a structure includes:
+</p>
+
+<div data-title="Component 2 (objects)" data-count="2" class="component" id="objects"><div class="ruleTitle"><a href="#objects" class="internalDFN">Component 2 (objects)</a></div>
+ <ol><li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-34-Frame" class="MathJax"><nobr><span id="MathJax-Span-1567" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1568" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1569" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1570" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1571" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1572" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1573" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1575" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-34" type="math/tex">Objects</script>
+</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-35-Frame" class="MathJax"><nobr><span id="MathJax-Span-1576" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1577" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1578" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1579" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1580" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1581" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1582" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1583" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1584" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1585" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1586" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1587" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1588" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1589" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1591" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1592" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1593" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1594" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1595" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1596" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1598" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1599" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1600" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1601" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1602" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1603" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-35" type="math/tex">lifetime : Objects \to Intervals</script> from objects to time intervals
+</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-36-Frame" class="MathJax"><nobr><span id="MathJax-Span-1604" class="math"><span style="display: inline-block; position: relative; width: 291px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1605" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1606" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1607" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1608" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1609" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1610" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1611" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1612" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1613" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1614" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1615" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1616" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1618" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-1619" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-1620" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1621" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1622" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1623" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1624" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1625" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1626" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1628" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1629" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1630" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1631" class="mi">P</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1632" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1633" class="mi">V<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1634" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1635" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1636" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1637" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1638" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1639" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-36" type="math/tex">value : Objects \times Attributes \to P(Values)</script>
+</li></ol>
+</div>
+
+<p>Intuitively, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-37-Frame" class="MathJax"><nobr><span id="MathJax-Span-1640" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1641" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1642" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1643" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1644" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1645" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1646" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1647" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1648" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1649" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1650" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1651" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1652" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-37" type="math/tex">lifetime(e)</script> is the time interval during which object
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-38-Frame" class="MathJax"><nobr><span id="MathJax-Span-1653" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1654" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1655" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-38" type="math/tex">e</script> exists. The set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-39-Frame" class="MathJax"><nobr><span id="MathJax-Span-1656" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1657" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1658" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1660" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1662" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1663" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1664" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1665" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1666" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1667" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-39" type="math/tex">value(e,a)</script> is the set of values of attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-40-Frame" class="MathJax"><nobr><span id="MathJax-Span-1668" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1669" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1670" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-40" type="math/tex">a</script> during the object's lifetime.
+</p>
+
+<p>As with <em>Things</em>, the range of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-41-Frame" class="MathJax"><nobr><span id="MathJax-Span-1671" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1672" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1673" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1674" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1675" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1676" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1677" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-41" type="math/tex">value</script> is sets of values,
+making <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-42-Frame" class="MathJax"><nobr><span id="MathJax-Span-1678" class="math"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1679" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1680" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1681" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1682" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1683" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1684" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-42" type="math/tex">value</script> effectively a multivalued function. It is also possible to have two different objects that are indistinguishable by their attributes and time intervals. Objects are not things, and the sets of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-43-Frame" class="MathJax"><nobr><span id="MathJax-Span-1685" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1686" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1687" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1688" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1689" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1690" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1691" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1693" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-43" type="math/tex">Objects</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-44-Frame" class="MathJax"><nobr><span id="MathJax-Span-1694" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1695" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1696" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1697" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1698" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1699" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1700" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1701" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-44" type="math/tex">Things</script> are disjoint; however, certain objects, namely entities, are linked to things.
+
+</p>
+<section id="entities-1">
+<h4><span class="secno">3.2.1 </span> Entities </h4>
+
+An <em>entity</em> is a kind of object that describes a time-slice of a thing, during which some of the thing's attributes are fixed. We assume:
+
+<div data-title="Component 3 (entities)" data-count="3" class="component" id="entities"><div class="ruleTitle"><a href="#entities" class="internalDFN">Component 3 (entities)</a></div>
+ <ol><li> a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-45-Frame" class="MathJax"><nobr><span id="MathJax-Span-1702" class="math"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1703" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1704" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1705" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1706" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1707" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1709" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1710" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1711" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1712" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1713" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1714" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1715" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1717" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1719" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-45" type="math/tex">Entities \subseteq Objects</script> of entities, disjoint from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-46-Frame" class="MathJax"><nobr><span id="MathJax-Span-1720" class="math"><span style="display: inline-block; position: relative; width: 64px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.763em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1721" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1722" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1723" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1725" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1726" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1728" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1729" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1730" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1731" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.859em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-46" type="math/tex">Activities</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-47-Frame" class="MathJax"><nobr><span id="MathJax-Span-1732" class="math"><span style="display: inline-block; position: relative; width: 46px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1733" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1734" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1735" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1736" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1737" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1739" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-47" type="math/tex">Events</script> below.
+</li><li> a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-48-Frame" class="MathJax"><nobr><span id="MathJax-Span-1740" class="math"><span style="display: inline-block; position: relative; width: 199px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1741" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1742" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1743" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1744" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1745" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1746" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1747" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1748" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1749" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1750" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1751" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1753" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1754" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1755" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1757" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1758" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1759" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1760" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1762" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1763" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1764" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-48" type="math/tex">thingOf : Entities \to Things</script> that associates each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-49-Frame" class="MathJax"><nobr><span id="MathJax-Span-1765" class="math"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1766" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1767" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1768" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1772" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-49" type="math/tex">Entity</script> with a <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-50-Frame" class="MathJax"><nobr><span id="MathJax-Span-1773" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1774" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1775" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1776" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1778" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1779" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-50" type="math/tex">Thing</script>, such that for each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-51-Frame" class="MathJax"><nobr><span id="MathJax-Span-1780" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1781" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1783" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1784" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1785" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1786" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1787" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1789" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1790" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1791" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1792" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1793" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1794" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1795" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1796" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-51" type="math/tex">t \in lifetime(obj)</script>, and for each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-52-Frame" class="MathJax"><nobr><span id="MathJax-Span-1797" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1798" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1799" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-52" type="math/tex">a</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-53-Frame" class="MathJax"><nobr><span id="MathJax-Span-1800" class="math"><span style="display: inline-block; position: relative; width: 274px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1801" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1802" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1803" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1804" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1805" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1806" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1807" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1808" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1809" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1810" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1811" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1812" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1813" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1814" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1815" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1816" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1817" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1818" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1819" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1820" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1822" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1823" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1825" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1826" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1827" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1829" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1830" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1831" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1832" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1833" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1834" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1835" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1837" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-53" type="math/tex">value(obj,a) \subseteq value(thingOf(obj),a,t)</script>.
+</li><li> <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-54-Frame" class="MathJax"><nobr><span id="MathJax-Span-1838" class="math"><span style="display: inline-block; position: relative; width: 166px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1839" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1840" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1841" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1842" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1843" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1845" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1846" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1847" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1848" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1849" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1850" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1851" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1852" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1853" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1854" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1855" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1856" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1857" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1858" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1859" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1860" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1861" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1862" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-54" type="math/tex">lifetime(e) \subseteq lifetime(t)</script>.
+</li></ol>
+</div>
+
+<div class="remark"><p> Although both entities and things can have
+ undefined or multiple attribute values, their meaning is slightly
+ different: for a thing, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-55-Frame" class="MathJax"><nobr><span id="MathJax-Span-1863" class="math"><span style="display: inline-block; position: relative; width: 116px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1864" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1865" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1866" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1867" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1868" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1869" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1870" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1871" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1872" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1873" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1874" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1875" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1876" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1877" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1878" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-55" type="math/tex">value(x,a,t) = \emptyset</script> means that the
+ attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-56-Frame" class="MathJax"><nobr><span id="MathJax-Span-1879" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1880" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1881" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-56" type="math/tex">a</script> has no value at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-57-Frame" class="MathJax"><nobr><span id="MathJax-Span-1882" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1883" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-57" type="math/tex">t</script>, whereas for an entity,
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-58-Frame" class="MathJax"><nobr><span id="MathJax-Span-1885" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1886" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1887" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1888" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1889" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1890" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1891" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1892" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1893" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1894" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1895" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1896" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1897" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1898" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.094em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-58" type="math/tex">value(x,a) = \emptyset</script> only means that the entity does not record
+ a fixed value for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-59-Frame" class="MathJax"><nobr><span id="MathJax-Span-1899" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1900" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1901" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-59" type="math/tex">a</script> forthe associated thing. This does not imply
+ that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-60-Frame" class="MathJax"><nobr><span id="MathJax-Span-1902" class="math"><span style="display: inline-block; position: relative; width: 182px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1904" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1905" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1906" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1907" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1908" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1909" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1910" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1911" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1912" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1913" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1914" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1915" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1916" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1917" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1918" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1919" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1920" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1921" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1922" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1923" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1924" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1925" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-1926" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.127em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-60" type="math/tex">value(thingOf(e),a,t) = \emptyset</script> when <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-61-Frame" class="MathJax"><nobr><span id="MathJax-Span-1927" class="math"><span style="display: inline-block; position: relative; width: 100px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1928" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-1930" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-1931" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1932" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1933" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1934" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1935" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1936" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1937" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1938" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1939" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1940" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1941" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-61" type="math/tex">t \in lifetime(e)</script>.
+</p>
+ <p>Furthermore, all of the attribute values of the entity must be
+ present in the associated thing throughout the lifetime of the entity.
+For example, suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-62-Frame" class="MathJax"><nobr><span id="MathJax-Span-1942" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1943" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1944" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1945" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1946" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1947" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1948" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1949" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1950" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1951" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1952" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1953" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1954" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1955" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1956" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1957" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1958" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1959" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1961" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1962" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-1963" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1964" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-62" type="math/tex">value(thingOf(e),a,t)</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-63-Frame" class="MathJax"><nobr><span id="MathJax-Span-1965" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1966" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-1967" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1968" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1969" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-63" type="math/tex">\{1\}</script> at some
+time in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-64-Frame" class="MathJax"><nobr><span id="MathJax-Span-1970" class="math"><span style="display: inline-block; position: relative; width: 73px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1971" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1972" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1973" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1974" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1975" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1976" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1978" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1979" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1980" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1981" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1982" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-64" type="math/tex">lifetime(e)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-65-Frame" class="MathJax"><nobr><span id="MathJax-Span-1983" class="math"><span style="display: inline-block; position: relative; width: 202px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.632em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-1984" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1985" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1987" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1988" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1989" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-1990" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1992" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1995" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1996" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1997" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-1998" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-1999" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2000" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2001" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2002" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2003" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-2004" class="msup"><span style="display: inline-block; position: relative; width: 0.656em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.466em; left: 0.347em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-2006" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2007" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2008" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2009" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2010" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2011" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.162em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-65" type="math/tex">value(thingOf(e),a,t') = \{2\}</script> at some
+ other time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-66-Frame" class="MathJax"><nobr><span id="MathJax-Span-2012" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.107em, 1000em, 2.231em, -0.488em); top: -2.044em; left: 0em;"><span id="MathJax-Span-2013" class="mrow"><span id="MathJax-Span-2014" class="msup"><span style="display: inline-block; position: relative; width: 0.656em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.466em; left: 0.347em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-2016" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.953em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-66" type="math/tex">t'</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-67-Frame" class="MathJax"><nobr><span id="MathJax-Span-2017" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2018" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2019" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2021" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2022" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2023" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2024" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2025" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2027" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2028" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-67" type="math/tex">value(e,a)</script> must be <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-68-Frame" class="MathJax"><nobr><span id="MathJax-Span-2029" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.819em, -0.498em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2030" class="mrow"><span style="font-family: STIXVariants;" id="MathJax-Span-2031" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.984em; vertical-align: -0.142em;"></span></span></nobr></span><script id="MathJax-Element-68" type="math/tex">\emptyset</script> because
+ there is no other set of values that is simultaneously contained in
+ both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-69-Frame" class="MathJax"><nobr><span id="MathJax-Span-2032" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2033" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2034" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2035" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2036" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-69" type="math/tex">\{1\}</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-70-Frame" class="MathJax"><nobr><span id="MathJax-Span-2037" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.926em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2038" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2039" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2040" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2041" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.046em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-70" type="math/tex">\{2\}</script>.
+</p>
+ </div>
+
+<section id="plans-1">
+<h5><span class="secno">3.2.1.1 </span> Plans </h5>
+<p>We identify a specific subset of the entities called
+ <em>plans</em>:
+</p><div data-title="Component 4 (plans)" data-count="4" class="component" id="plans"><div class="ruleTitle"><a href="#plans" class="internalDFN">Component 4 (plans)</a></div>
+ <p> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-71-Frame" class="MathJax"><nobr><span id="MathJax-Span-2042" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2043" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2044" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2045" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2046" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2047" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2048" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2049" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2050" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2051" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2053" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2054" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2055" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2056" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2057" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-71" type="math/tex">Plans \subseteq Entities</script> of plans.</p>
+ </div>
+<p></p></section>
+
+ </section>
+
+ <section id="actvities">
+<h4><span class="secno">3.2.2 </span> Actvities </h4>
+
+
+<p>An <em>activity</em> is an object that encompasses a set of events. We introduce
+</p>
+<div data-title="Component 5 (activities)" data-count="5" class="component" id="activities"><div class="ruleTitle"><a href="#activities" class="internalDFN">Component 5 (activities)</a></div>
+ <ol><li>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-72-Frame" class="MathJax"><nobr><span id="MathJax-Span-2058" class="math"><span style="display: inline-block; position: relative; width: 139px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2059" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2060" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2061" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2064" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2065" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2066" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2067" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2069" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2070" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2071" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2072" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2073" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2075" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2076" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2077" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-72" type="math/tex">Activities \subseteq Objects</script> of activities.</li>
+ <li> Activities are disjoint from Entities: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-73-Frame" class="MathJax"><nobr><span id="MathJax-Span-2078" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.819em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2079" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2080" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2081" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2082" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2085" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2086" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2087" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2088" class="mo">∩</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2089" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2090" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2091" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2092" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2093" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2094" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2096" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2097" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2098" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2099" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-2100" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.984em; vertical-align: -0.142em;"></span></span></nobr></span><script id="MathJax-Element-73" type="math/tex">Entities\cap Activities
+ = \emptyset</script>.</li>
+ </ol>
+</div></section>
+
+ <section id="agents-1">
+<h4><span class="secno">3.2.3 </span> Agents </h4>
+
+<p>An agent is an object that can act, by controlling, starting,
+ ending, or participating in activities. Agents can act on behalf of
+ other agents. An agent can be an entity, an activity, or neither; an
+ agent cannot be both entity and activity because the sets of
+ entities and activities are disjoint. We introduce:
+</p>
+<div data-title="Component 6 (agents)" data-count="6" class="component" id="agents"><div class="ruleTitle"><a href="#agents" class="internalDFN">Component 6 (agents)</a></div>
+ <p>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-74-Frame" class="MathJax"><nobr><span id="MathJax-Span-2101" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2102" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2103" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2104" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2105" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2106" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2108" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2109" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2110" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2111" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2112" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2113" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2114" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2116" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-74" type="math/tex">Agents \subseteq Objects</script> of agents.</p>
+ </div>
+</section>
+
+
+<section id="interactions-1">
+<h4><span class="secno">3.2.4 </span> Interactions </h4>
+
+<p>We consider a set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-75-Frame" class="MathJax"><nobr><span id="MathJax-Span-2117" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2118" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2119" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2120" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2121" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2123" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2124" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2125" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2126" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2127" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2129" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2130" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2131" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2132" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2133" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2134" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2135" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2136" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2137" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2138" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-75" type="math/tex">Interactions \subseteq Objects</script> which are split into
+ <em>Events</em> connecting entities and activities,
+ <em>Associations</em> between agents and activities,
+ <em>Communications</em> between pairs of activities,
+ <em>Delegations</em> between pairs of agents, and <em>Derivations</em> that describe chains of generation and usage steps. (The first two sets may overlap.) Interactions are disjoint from entities, activities and agents.
+</p>
+<div data-title="Component 7 (interactions)" data-count="7" class="component" id="interactions"><div class="ruleTitle"><a href="#interactions" class="internalDFN">Component 7 (interactions)</a></div>
+ <ol><li> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-76-Frame" class="MathJax"><nobr><span id="MathJax-Span-2139" class="math"><span style="display: inline-block; position: relative; width: 672px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2141" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2142" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2143" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2145" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2146" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2147" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2149" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2150" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2151" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2152" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2153" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2154" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2155" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2156" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2157" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2159" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2160" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2161" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2162" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2163" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2164" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2165" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2166" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2167" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2168" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2169" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2170" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2171" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2172" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2173" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2174" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2175" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2176" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2177" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2178" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2179" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2180" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2181" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2183" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2184" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2185" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2186" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2187" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2188" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2189" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2190" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2191" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2193" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2194" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2195" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2197" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2198" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2199" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2200" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2201" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2203" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2204" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2205" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2208" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2209" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2210" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2211" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2212" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2213" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2214" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2215" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2216" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2217" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2218" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2219" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-76" type="math/tex">Interactions = Events \cup Associations \cup
+ Communications \cup Delegations \cup Derivations \subseteq Objects</script>
+</li>
+<li> A function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-77-Frame" class="MathJax"><nobr><span id="MathJax-Span-2220" class="math"><span style="display: inline-block; position: relative; width: 939px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.954em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2221" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2222" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2223" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2224" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2225" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2226" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2227" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2228" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2230" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2231" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2232" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2233" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2236" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2237" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2238" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2239" class="mo">→</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2240" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2241" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2242" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2244" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2248" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2249" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2250" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2251" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2252" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2253" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2254" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2255" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2256" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2257" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2258" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2259" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2260" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2261" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2262" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2264" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2265" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2266" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2268" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2269" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2270" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2272" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2273" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2274" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2275" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2276" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2277" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2278" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2279" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2280" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2281" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2282" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2283" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2284" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2285" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2288" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2289" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2290" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2291" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2292" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2293" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2294" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2295" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2296" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2297" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2298" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2300" class="mi">q</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2301" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2303" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2304" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2306" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2307" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2308" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2309" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2310" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2312" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2313" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2315" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2316" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2317" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2318" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2319" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2320" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2321" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2322" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2324" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2325" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2326" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2327" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2328" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2329" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2330" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2331" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2332" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2333" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2334" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2335" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2336" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2338" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2339" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2340" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2341" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2342" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2343" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2344" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2345" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2346" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.079em; vertical-align: -0.286em;"></span></span></nobr></span><script id="MathJax-Element-77" type="math/tex">type: Interactions \to
+ \{start,end,usage,generation,invalidation,derivation,version,quotation,primarySource,attribution,delegation\}</script>.
+</li>
+<li> The sets <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-78-Frame" class="MathJax"><nobr><span id="MathJax-Span-2347" class="math"><span style="display: inline-block; position: relative; width: 46px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2348" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2349" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2350" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2351" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2352" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2353" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2354" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-78" type="math/tex">Events</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-79-Frame" class="MathJax"><nobr><span id="MathJax-Span-2355" class="math"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2356" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2357" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2358" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2359" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2360" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2361" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2362" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2365" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2366" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2367" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2368" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-79" type="math/tex">Associations</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-80-Frame" class="MathJax"><nobr><span id="MathJax-Span-2369" class="math"><span style="display: inline-block; position: relative; width: 117px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.729em, 1000em, 2.763em, -0.46em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2370" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2371" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2372" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2373" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2374" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2375" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2376" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2377" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2378" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2379" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2380" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2381" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2382" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2383" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2384" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.857em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-80" type="math/tex">Communications</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-81-Frame" class="MathJax"><nobr><span id="MathJax-Span-2385" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2386" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2387" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2389" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2390" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2391" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2392" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2393" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2394" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2395" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2396" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2397" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-81" type="math/tex">Delegations</script>
+ and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-82-Frame" class="MathJax"><nobr><span id="MathJax-Span-2398" class="math"><span style="display: inline-block; position: relative; width: 81px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.763em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2399" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2400" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2401" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2402" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2403" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2404" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2405" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2406" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2407" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2408" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2409" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2410" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.844em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-82" type="math/tex">Derivations</script> are all disjoint.
+</li><li> Interactions are disjoint from entities, agents and
+activities: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-83-Frame" class="MathJax"><nobr><span id="MathJax-Span-2411" class="math"><span style="display: inline-block; position: relative; width: 348px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.666em, 1000em, 2.951em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2412" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2413" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2414" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2416" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2417" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2418" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2419" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2420" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2421" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2422" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2423" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2424" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2425" class="mo">∩</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2426" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2427" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2428" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2429" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2430" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2432" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2433" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2434" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2435" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2436" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2437" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2438" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2439" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2440" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2441" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2442" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2443" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2444" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2445" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2446" class="mo">∪</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2447" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2448" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2449" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2450" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2452" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2453" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2454" class="mo">=</span><span style="font-family: STIXVariants; padding-left: 0.313em;" id="MathJax-Span-2455" class="mi">∅</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.125em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-83" type="math/tex">Interactions \cap (Entities \cup Activities \cup Agents) = \emptyset</script>
+</li></ol>
+</div>
+
+<section id="events-1">
+<h5><span class="secno">3.2.4.1 </span> Events </h5>
+
+<p>An <em>Event</em> is an interaction whose lifetime is a single time
+instant, and relates an activity to an entity (which could be an
+agent). Events have types including usage, generation, invalidation, starting and ending. Events are instantaneous. We introduce:
+</p>
+<div data-title="Component 8 (events)" data-count="8" class="component" id="events"><div class="ruleTitle"><a href="#events" class="internalDFN">Component 8 (events)</a></div>
+<ol><li> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-84-Frame" class="MathJax"><nobr><span id="MathJax-Span-2456" class="math"><span style="display: inline-block; position: relative; width: 153px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2457" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2458" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2459" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2460" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2461" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2462" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2463" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2464" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2465" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2466" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2468" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2469" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2471" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2472" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2473" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2474" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2475" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2476" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.935em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-84" type="math/tex">Events \subseteq Interactions</script> of events, such that
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-85-Frame" class="MathJax"><nobr><span id="MathJax-Span-2477" class="math"><span style="display: inline-block; position: relative; width: 381px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2478" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2480" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2481" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2482" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2483" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2485" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2486" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2487" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2488" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2489" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2490" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2491" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2492" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2493" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2494" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2495" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2496" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2497" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2498" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2499" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2500" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2502" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2503" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2504" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2505" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2506" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2507" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2508" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2509" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2511" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2512" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2513" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2514" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2515" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2516" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2517" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2518" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2519" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2520" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2521" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2522" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2523" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2524" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2527" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2528" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2529" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-85" type="math/tex">type(evt) \in \{start,end,generation,usage,invalidation\}</script> if and
+ only of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-86-Frame" class="MathJax"><nobr><span id="MathJax-Span-2530" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.772em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2531" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2532" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2533" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2535" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2536" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2537" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2538" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2539" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2541" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-86" type="math/tex">evt \in Events</script>.
+</li><li> A function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-87-Frame" class="MathJax"><nobr><span id="MathJax-Span-2542" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.763em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2543" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2546" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2547" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2548" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2549" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2550" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2551" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2552" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2554" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2555" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2556" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2557" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2558" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2559" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2560" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.844em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-87" type="math/tex">time : Events \to Times</script> giving the time of each event; i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-88-Frame" class="MathJax"><nobr><span id="MathJax-Span-2561" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2562" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2563" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2565" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2566" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2567" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2568" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2569" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2570" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2571" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2572" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2573" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2575" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2576" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2577" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2579" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2580" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2581" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2582" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2584" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2585" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-88" type="math/tex">lifetime(evt) = \{time(t)\}</script>.
+</li><li> The derived ordering on events given by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-89-Frame" class="MathJax"><nobr><span id="MathJax-Span-2586" class="math"><span style="display: inline-block; position: relative; width: 284px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2587" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2588" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2589" class="mi">v</span><span id="MathJax-Span-2590" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2591" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2592" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2593" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2595" class="mi">v</span><span id="MathJax-Span-2596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2598" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="height: 0em; vertical-align: 0em; width: 0.313em; display: inline-block; overflow: hidden;" id="MathJax-Span-2599" class="mspace"></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2600" class="mo">⟺</span><span style="height: 0em; vertical-align: 0em; width: 0.313em; display: inline-block; overflow: hidden;" id="MathJax-Span-2601" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2603" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2604" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2605" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2606" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2607" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2608" class="mi">v</span><span id="MathJax-Span-2609" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2610" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2611" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2612" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2613" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2614" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2615" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2616" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2617" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2618" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2620" class="mi">v</span><span id="MathJax-Span-2621" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2622" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-2623" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2624" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-89" type="math/tex">evt_1 \leq evt_2 \iff time(evt_1) \leq time(evt_2)</script>
+</li></ol>
+</div>
+</section>
+<section id="associations-1">
+
+<h5><span class="secno">3.2.4.2 </span> Associations </h5>
+
+<p>An <em>Association</em> is an interaction relating an agent to an activity. To model associations, we introduce:
+</p>
+<div data-title="Component 9 (associations)" data-count="9" class="component" id="associations"><div class="ruleTitle"><a href="#associations" class="internalDFN">Component 9 (associations)</a></div>
+ <p>A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-90-Frame" class="MathJax"><nobr><span id="MathJax-Span-2625" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.848em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2626" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2627" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2628" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2629" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2630" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2631" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2632" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2633" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2634" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2635" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2636" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2637" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2638" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2639" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2640" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2641" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2642" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2643" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2644" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2645" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2647" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2648" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2649" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2650" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2651" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.95em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-90" type="math/tex">Associations \subseteq Interactions</script>, such that
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-91-Frame" class="MathJax"><nobr><span id="MathJax-Span-2652" class="math"><span style="display: inline-block; position: relative; width: 179px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2655" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2656" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2657" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2658" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2660" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2661" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2662" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2663" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2664" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2665" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2668" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2669" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2670" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2672" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2674" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2675" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2676" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-91" type="math/tex">type(assoc) = association</script> if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-92-Frame" class="MathJax"><nobr><span id="MathJax-Span-2677" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.772em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2678" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2680" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2681" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2682" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2683" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2684" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2685" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2686" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2687" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2688" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2689" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2690" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2691" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2693" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2694" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2695" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2696" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.869em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-92" type="math/tex">assoc \in Associations</script>.
+</p>
+ </div>
+
+<p>Associations are used below in the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-93-Frame" class="MathJax"><nobr><span id="MathJax-Span-2697" class="math"><span style="display: inline-block; position: relative; width: 56px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2698" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2699" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2700" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2701" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2702" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2703" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2704" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2705" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-93" type="math/tex">ActsFor</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-94-Frame" class="MathJax"><nobr><span id="MathJax-Span-2706" class="math"><span style="display: inline-block; position: relative; width: 109px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2707" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2708" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2709" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2710" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2711" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2712" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2713" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2714" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2715" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2717" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2718" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2719" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2720" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2721" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-94" type="math/tex">AssociatedWith</script> relations.
+
+
+</p></section>
+ <section id="communications">
+ <h5><span class="secno">3.2.4.3 </span>Communications</h5>
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO</div></div>
+
+</section>
+ <section id="delegations">
+ <h5><span class="secno">3.2.4.4 </span>Delegations</h5>
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO</div></div>
+</section>
+ <section id="derivations-1">
+
+ <h5><span class="secno">3.2.4.5 </span> Derivations </h5>
+
+<p>A <em>Derivation</em> is an interaction chaining one or more generation and use steps.
+</p>
+<div data-title="Component 10 (derivations)" data-count="10" class="component" id="derivations"><div class="ruleTitle"><a href="#derivations" class="internalDFN">Component 10 (derivations)</a></div>
+<p> A set <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-95-Frame" class="MathJax"><nobr><span id="MathJax-Span-2722" class="math"><span style="display: inline-block; position: relative; width: 188px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2723" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2724" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2725" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2726" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2728" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2729" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2730" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2731" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2732" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2733" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2734" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2735" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2736" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2737" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2740" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2741" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2742" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2743" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2744" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2745" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2746" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2747" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.935em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-95" type="math/tex">Derivations \subseteq Interactions</script>, such that
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-96-Frame" class="MathJax"><nobr><span id="MathJax-Span-2748" class="math"><span style="display: inline-block; position: relative; width: 427px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.954em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2749" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2750" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2751" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2752" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2753" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2754" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2755" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2757" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2758" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2759" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2760" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2761" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2762" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2763" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2764" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2765" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2766" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2767" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2768" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2771" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2772" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2773" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2774" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2775" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2776" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2777" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2778" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2779" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2780" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2781" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2782" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2783" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2784" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2785" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2786" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2787" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2788" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2789" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2790" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2791" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2792" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2793" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2794" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2795" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2796" class="mi">q</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2797" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2798" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2799" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2800" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2801" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2802" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2803" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2804" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2805" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.079em; vertical-align: -0.286em;"></span></span></nobr></span><script id="MathJax-Element-96" type="math/tex">type(deriv) \in \{derivation, version, primarySource,quotation\}</script>
+ if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-97-Frame" class="MathJax"><nobr><span id="MathJax-Span-2806" class="math"><span style="display: inline-block; position: relative; width: 140px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.772em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2807" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2808" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2809" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2810" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2812" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2813" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2814" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2815" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2816" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2818" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2819" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2820" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2821" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2822" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2823" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2824" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.885em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-97" type="math/tex">deriv \in Derivations</script>.
+</p></div>
+<p>See below for the associated derivation path and DerivedFrom relation.
+</p>
+</section>
+</section>
+</section>
+<section id="relations">
+
+<h3><span class="secno">3.3 </span> Relations </h3>
+
+<h3 id="simple-relations"> Simple relations </h3>
+<p>The entities, interactions, and activities in a structure are related in the following ways:
+</p>
+<ol><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-98-Frame" class="MathJax"><nobr><span id="MathJax-Span-2825" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.424em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2826" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2827" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2828" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2829" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2830" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2831" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2832" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2833" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2834" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2835" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2837" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2838" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2839" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2840" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2841" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2844" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2845" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2846" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-98" type="math/tex">Used \subseteq Events \times Entities</script> saying when an event used an entity. An event can use at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-99-Frame" class="MathJax"><nobr><span id="MathJax-Span-2847" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2848" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2849" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2851" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2853" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2854" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2855" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2856" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2857" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2858" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2859" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2860" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-99" type="math/tex">(evt,e)\in Used</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-100-Frame" class="MathJax"><nobr><span id="MathJax-Span-2861" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2862" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2864" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2865" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2866" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2867" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2868" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2869" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2870" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2871" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2872" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2873" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2875" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2876" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2877" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2878" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2879" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2880" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2881" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2882" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2883" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-100" type="math/tex">time(evt) \in lifetime(e)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-101-Frame" class="MathJax"><nobr><span id="MathJax-Span-2884" class="math"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2885" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2886" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2887" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2888" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2889" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2890" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2891" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2892" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2893" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2894" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2895" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2896" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-101" type="math/tex">type(g) = use</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-102-Frame" class="MathJax"><nobr><span id="MathJax-Span-2897" class="math"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.474em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2898" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2899" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2900" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2901" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2902" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2903" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2904" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2905" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2906" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2907" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2908" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2909" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2910" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2911" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2912" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2914" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-2915" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-2916" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2917" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2918" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2919" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2920" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2921" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2922" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2923" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-102" type="math/tex">Generated \subseteq Events \times Entities</script> saying when an event generated an entity. An event can generate at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-103-Frame" class="MathJax"><nobr><span id="MathJax-Span-2924" class="math"><span style="display: inline-block; position: relative; width: 143px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2925" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-2926" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2927" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2928" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2930" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-2931" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2932" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2933" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2934" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2935" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2936" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2939" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2941" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2942" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-103" type="math/tex">(evt,e)\in Generated</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-104-Frame" class="MathJax"><nobr><span id="MathJax-Span-2943" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2944" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2945" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2946" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2947" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2948" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2949" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2950" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2951" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2952" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2954" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2955" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2956" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2957" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2958" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2959" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2960" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2961" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2962" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2963" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2964" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2965" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2966" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2967" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2968" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2969" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-2970" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-104" type="math/tex">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-105-Frame" class="MathJax"><nobr><span id="MathJax-Span-2971" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2972" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2973" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2974" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2975" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2976" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2977" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2978" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-2979" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-2980" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-2981" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2982" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2983" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2984" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2987" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2988" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2989" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2990" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-105" type="math/tex">type(g) = generation</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-106-Frame" class="MathJax"><nobr><span id="MathJax-Span-2991" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-2992" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2993" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2995" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2996" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2997" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2998" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-2999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3000" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3001" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3002" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3003" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3004" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3005" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3006" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3007" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3008" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3010" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3011" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3012" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3013" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3017" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3018" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3019" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.966em; vertical-align: -0.173em;"></span></span></nobr></span><script id="MathJax-Element-106" type="math/tex">Invalidated \subseteq Events \times Entities</script> saying when an event invalidated an entity. An event can invalidate at most one entity, and if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-107-Frame" class="MathJax"><nobr><span id="MathJax-Span-3020" class="math"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3021" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3022" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3023" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3024" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3025" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3027" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3028" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3029" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3030" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3031" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3032" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3033" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3034" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3035" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3036" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3037" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3039" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3040" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-107" type="math/tex">(evt,e)\in Invalidated</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-108-Frame" class="MathJax"><nobr><span id="MathJax-Span-3041" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3042" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3043" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3044" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3045" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3046" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3047" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3048" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3049" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3050" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3051" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3052" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3053" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3054" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3055" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3056" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3057" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3058" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3059" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3061" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3062" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3063" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3064" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3066" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3068" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-108" type="math/tex">min(lifetime(e)) = time(evt)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-109-Frame" class="MathJax"><nobr><span id="MathJax-Span-3069" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3070" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3071" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3072" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3073" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3074" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3075" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3076" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3077" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3078" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3079" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3080" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3081" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3082" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3083" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3084" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3085" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3086" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3087" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3088" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3089" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3090" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-109" type="math/tex">type(g) = invalidation</script> must hold.
+</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-110-Frame" class="MathJax"><nobr><span id="MathJax-Span-3091" class="math"><span style="display: inline-block; position: relative; width: 245px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.951em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3092" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3093" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3094" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3095" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3096" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3097" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3098" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3099" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3100" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3102" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3103" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3104" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3105" class="mi">y</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3106" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3107" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3108" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3109" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3110" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3111" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3112" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3113" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3114" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3115" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3117" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3118" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3119" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3123" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.06em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-110" type="math/tex">EventActivity \subseteq Events \times Activities</script> associating activities with events, such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-111-Frame" class="MathJax"><nobr><span id="MathJax-Span-3124" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3125" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3126" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3127" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3128" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3130" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3131" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3132" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3134" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3135" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3136" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3137" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3138" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3139" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3141" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3142" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3143" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3144" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3145" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3146" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3147" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3148" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-111" type="math/tex">(act,evt) \in EventActivity</script> implies <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-112-Frame" class="MathJax"><nobr><span id="MathJax-Span-3149" class="math"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3150" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3152" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3153" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3154" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3155" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3156" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3157" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3159" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3160" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3161" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3162" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3163" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3164" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3165" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3166" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3167" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3168" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3169" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3171" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3173" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-112" type="math/tex">time(evt) \in lifetime(act)</script>.
+</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-113-Frame" class="MathJax"><nobr><span id="MathJax-Span-3174" class="math"><span style="display: inline-block; position: relative; width: 430px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3175" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3176" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3177" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3178" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3179" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3180" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3181" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3183" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3184" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3185" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3186" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3187" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3188" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3189" class="mi">h</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3190" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3191" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3192" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3193" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3194" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3195" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3197" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3199" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3200" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3201" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3202" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3203" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3204" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3205" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3206" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3208" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3209" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3210" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3211" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3213" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3214" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3215" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3217" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3218" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3219" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3220" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3221" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3222" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3223" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3224" class="mi">n</span><span id="MathJax-Span-3225" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3226" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3227" class="mi">⊥</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-113" type="math/tex">AssociatedWith \subseteq Association \times Agents \times Activities \times Plans_\bot</script> indicating when an agent is associated with an activity, and giving the identity of the association relationship, and an optional plan.
+</li><li> A relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-114-Frame" class="MathJax"><nobr><span id="MathJax-Span-3228" class="math"><span style="display: inline-block; position: relative; width: 377px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3229" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3230" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3231" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3232" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3233" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3234" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3235" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3236" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3237" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3238" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3239" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3240" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3241" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3242" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3246" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3247" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3248" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3249" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3250" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3251" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3252" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3253" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3255" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3256" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3257" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3258" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3259" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3260" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3262" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3263" class="mo">×</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3264" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3265" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3267" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3268" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3269" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3271" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3272" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3273" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-114" type="math/tex">ActsFor \subseteq Delegations \times Agents \times Agents \times Activities</script> indicating when one agent acts on behalf of another with respect to a given activity.
+</li></ol>
+
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ TODO: Communication, start, end relations
+ </div></div>
+
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ TODO: Specialization relation
+ </div></div>
+
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ TODO: Explicit axioms concerning the relations
+ </div></div>
+
+
+<section id="derivation-paths-and-derivedfrom">
+<h4><span class="secno">3.3.1 </span> Derivation paths and DerivedFrom </h4>
+
+<p>Recall that above we introduced a subset of interactions called <em>Derivations</em>. These identify <em>paths</em> of the form </p>
+
+<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-115-Frame" class="MathJax"><nobr><span id="MathJax-Span-3274" class="math"><span style="display: inline-block; position: relative; width: 388px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.993em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3275" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3276" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3277" class="mi">n</span><span id="MathJax-Span-3278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3280" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3281" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3283" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3284" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3285" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3287" class="mi">c</span><span id="MathJax-Span-3288" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3289" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3290" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3291" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3292" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3293" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3294" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3295" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3296" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3297" class="mi">n</span><span id="MathJax-Span-3298" class="msubsup"><span style="display: inline-block; position: relative; width: 1.517em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3299" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span id="MathJax-Span-3300" class="texatom"><span id="MathJax-Span-3301" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3302" class="mi">n</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3303" class="mo">−</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3304" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3305" class="mo">⋅</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3306" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3307" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3308" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3309" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3311" class="mi">n</span><span id="MathJax-Span-3312" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3314" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3315" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3316" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3317" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3318" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3319" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3321" class="mi">c</span><span id="MathJax-Span-3322" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3324" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3325" class="mo">⋅</span><span style="padding-left: 0.25em;" id="MathJax-Span-3326" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3327" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3328" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3329" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3330" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3331" class="mi">n</span><span id="MathJax-Span-3332" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3333" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3334" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.974em; vertical-align: -0.328em;"></span></span></nobr></span></div><script id="MathJax-Element-115" type="math/tex; mode=display">ent_n\cdot g_n\cdot act_n\cdot u_n\cdot ent_{n-1}\cdot ...\cdot
+ent_1\cdot g_1\cdot act_1\cdot u_1\cdot ent_0</script>
+
+<p>where the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-116-Frame" class="MathJax"><nobr><span id="MathJax-Span-3335" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3336" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3338" class="mi">n</span><span id="MathJax-Span-3339" class="msubsup"><span style="display: inline-block; position: relative; width: 0.524em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3340" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3341" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-116" type="math/tex">ent_i</script> are entities, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-117-Frame" class="MathJax"><nobr><span id="MathJax-Span-3342" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3343" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3344" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3345" class="mi">c</span><span id="MathJax-Span-3346" class="msubsup"><span style="display: inline-block; position: relative; width: 0.524em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3348" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-117" type="math/tex">act_i</script> are activities, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-118-Frame" class="MathJax"><nobr><span id="MathJax-Span-3349" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.469em, -0.518em); top: -2.044em; left: 0em;"><span id="MathJax-Span-3350" class="mrow"><span id="MathJax-Span-3351" class="msubsup"><span style="display: inline-block; position: relative; width: 0.776em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3352" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3353" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.863em; vertical-align: -0.329em;"></span></span></nobr></span><script id="MathJax-Element-118" type="math/tex">g_i</script> are generations, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-119-Frame" class="MathJax"><nobr><span id="MathJax-Span-3354" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.377em, -0.484em); top: -2.044em; left: 0em;"><span id="MathJax-Span-3355" class="mrow"><span id="MathJax-Span-3356" class="msubsup"><span style="display: inline-block; position: relative; width: 0.776em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3357" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3358" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.766em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-119" type="math/tex">u_i</script> are usages.
+</p>
+<p>Formally, we consider the (regular) language:
+</p>
+<span class="MathJax_Preview"></span><div style="text-align: center;" aria-readonly="true" role="textbox" class="MathJax_Display"><span style="" id="MathJax-Element-120-Frame" class="MathJax"><nobr><span id="MathJax-Span-3359" class="math"><span style="display: inline-block; position: relative; width: 473px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.595em, 1000em, 2.922em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3360" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3361" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3362" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3363" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3364" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3365" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3366" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3367" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3368" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3369" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3370" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3371" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3372" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3373" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3374" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3375" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3376" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3377" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3378" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3379" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3380" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3381" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3382" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3383" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3384" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3385" class="mo">⋅</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3386" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3387" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3388" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3389" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3390" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3392" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3393" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3394" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3395" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3397" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3398" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3399" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3400" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3401" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3402" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3403" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3404" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3405" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3406" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3408" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3409" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3410" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3411" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3412" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3413" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3415" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3416" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3417" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3418" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3419" class="mi">s</span><span id="MathJax-Span-3420" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.497em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-3421" class="mo">)</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.516em; left: 0.35em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3422" class="mo">+</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.17em; vertical-align: -0.252em;"></span></span></nobr></span></div><script id="MathJax-Element-120" type="math/tex; mode=display">DerivationPaths = Entities \cdot (Events \cdot Activities \cdot
+Events \cdot Entities)^+</script>
+<p>with the constraints that for each derivation path:
+</p>
+<ul>
+<li>for each substring <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-121-Frame" class="MathJax"><nobr><span id="MathJax-Span-3423" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3424" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3425" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3426" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3428" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3429" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3430" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3431" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3432" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3433" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-121" type="math/tex">ent\cdot g \cdot act</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-122-Frame" class="MathJax"><nobr><span id="MathJax-Span-3434" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3435" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3436" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3437" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3438" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3439" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3440" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3441" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3442" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3443" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3444" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3445" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3446" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3447" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3448" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3449" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3451" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3452" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-122" type="math/tex">(g,ent) \in Generated</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-123-Frame" class="MathJax"><nobr><span id="MathJax-Span-3453" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3454" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3455" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3456" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3457" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3459" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3460" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3461" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3462" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3463" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3464" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3465" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3466" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3468" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3469" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3470" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3471" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3472" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3473" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3475" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3476" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3477" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-123" type="math/tex">(g,act) \in EventActivities</script>, and
+</li>
+<li>for each substring <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-124-Frame" class="MathJax"><nobr><span id="MathJax-Span-3478" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3479" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3480" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3481" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3483" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3484" class="mi">u</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3485" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3486" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3487" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-124" type="math/tex">act \cdot u \cdot ent</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-125-Frame" class="MathJax"><nobr><span id="MathJax-Span-3489" class="math"><span style="display: inline-block; position: relative; width: 107px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3490" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3491" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3492" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3493" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3494" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3495" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3496" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3497" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3498" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3499" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3500" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3502" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-125" type="math/tex">(u,ent) \in Used</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-126-Frame" class="MathJax"><nobr><span id="MathJax-Span-3503" class="math"><span style="display: inline-block; position: relative; width: 175px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3504" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3505" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3506" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3507" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3509" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3511" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3512" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3513" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3514" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3515" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3516" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3517" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3518" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3519" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3520" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3521" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3522" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3523" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3525" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3526" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3527" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-126" type="math/tex">(u,act) \in EventActivities</script>.
+</li>
+</ul>
+<p>We also consider a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-127-Frame" class="MathJax"><nobr><span id="MathJax-Span-3528" class="math"><span style="display: inline-block; position: relative; width: 329px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3529" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3530" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3531" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3532" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3533" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3534" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3535" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3536" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3537" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3539" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3540" class="mi">m</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3541" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3542" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3543" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3544" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3546" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3547" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3549" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3550" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3551" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3552" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3553" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3554" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3555" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3556" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3557" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3558" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3560" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3561" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3562" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3563" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3564" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3565" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3566" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3567" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3568" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-127" type="math/tex">derivedFrom : Derivations \to
+DerivationPaths</script> linking each derivation to its path.</p>
+
+
+<div class="remark">The reason why we need paths and not just individual derivation steps is that imprecise wasDerivedFrom formulas can represent multiple derivation steps.</div>
+</section>
+</section>
+
+<section id="putting-it-all-together">
+<h3><span class="secno">3.4 </span> Putting it all together </h3>
+
+<p>A <em>structure</em> <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-128-Frame" class="MathJax"><nobr><span id="MathJax-Span-3569" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3570" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3571" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-128" type="math/tex">W</script> is a structure containing all of the above
+described data. If we need to talk about the objects or relations of
+more than one structure then we may write <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-129-Frame" class="MathJax"><nobr><span id="MathJax-Span-3572" class="math"><span style="display: inline-block; position: relative; width: 82px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3573" class="mrow"><span id="MathJax-Span-3574" class="msubsup"><span style="display: inline-block; position: relative; width: 1.287em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3575" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.862em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3576" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3577" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3578" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3579" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3580" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3581" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3582" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3584" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-129" type="math/tex">W_1.Objects</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-130-Frame" class="MathJax"><nobr><span id="MathJax-Span-3585" class="math"><span style="display: inline-block; position: relative; width: 77px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3586" class="mrow"><span id="MathJax-Span-3587" class="msubsup"><span style="display: inline-block; position: relative; width: 1.287em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3588" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.862em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3589" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3590" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3591" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3592" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3593" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3594" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3595" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3596" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-130" type="math/tex">W_1.Things</script>,
+etc.; otherwise, to
+decrease notational clutter, when we consider a fixed structure then the names of the sets, relations and functions above refer to the components of that model.
+</p>
+
+</section>
+<section id="interpretations">
+<h3><span class="secno">3.5 </span> Interpretations </h3>
+
+<p>We need to link identifiers to the objects they denote. We do this using a function which we shall call an <em>interpretation</em>.
+ Thus, we consider interpretations as follows:
+An interpretation is a function <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-131-Frame" class="MathJax"><nobr><span id="MathJax-Span-3597" class="math"><span style="display: inline-block; position: relative; width: 179px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3598" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3599" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3600" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3601" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3602" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3603" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3604" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3606" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3607" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3608" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3610" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3611" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3612" class="mo">→</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3613" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3614" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3615" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3616" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3617" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3619" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-131" type="math/tex">\rho : Identifiers \to Objects</script> describing
+which object is the target of each identifier. The mapping from identifiers to objects may <b>not</b> change over time.
+</p>
+</section>
+
+</section>
+<section id="semantics">
+<!--OddPage--><h2><span class="secno">4. </span> Semantics </h2>
+
+<p>In what follows, let <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-132-Frame" class="MathJax"><nobr><span id="MathJax-Span-3620" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3621" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3622" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-132" type="math/tex">W</script> be a fixed structure with the associated sets and relations discussed in the previous section, and let <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-133-Frame" class="MathJax"><nobr><span id="MathJax-Span-3623" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3624" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3625" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-133" type="math/tex">I</script> be an interpretation of identifiers as objects in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-134-Frame" class="MathJax"><nobr><span id="MathJax-Span-3626" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3627" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3628" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-134" type="math/tex">W</script>.
+The annotations [WF] refer to well-formedness constraints that correspond to typing constraints.
+</p>
+
+<section id="satisfaction">
+<h3><span class="secno">4.1 </span> Satisfaction </h3>
+
+<p>Consider a formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-135-Frame" class="MathJax"><nobr><span id="MathJax-Span-3629" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3630" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3631" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-135" type="math/tex">\phi</script>, a structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-136-Frame" class="MathJax"><nobr><span id="MathJax-Span-3632" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3633" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3634" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-136" type="math/tex">W</script> and an interpretation
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-137-Frame" class="MathJax"><nobr><span id="MathJax-Span-3635" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3636" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3637" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-137" type="math/tex">I</script>.
+We define notation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-138-Frame" class="MathJax"><nobr><span id="MathJax-Span-3638" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3639" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3640" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3641" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3642" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3643" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3644" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-138" type="math/tex">W,\rho \models \phi</script> which means that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-139-Frame" class="MathJax"><nobr><span id="MathJax-Span-3645" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3646" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3647" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-139" type="math/tex">\phi</script> is
+ satisfied in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-140-Frame" class="MathJax"><nobr><span id="MathJax-Span-3648" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3649" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3650" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3651" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3652" class="mi">ρ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.043em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-140" type="math/tex">W,\rho</script>. For atomic formulas, the definition of the
+ satisfaction relation is given in the next few subsections. We give
+ the standard definition of the semantics of the other formulas:
+</p>
+
+<div data-title="Formalism 11 (first-order-logic)" data-count="11" class="formalism" id="first-order-logic"><div class="ruleTitle"><a href="#first-order-logic" class="internalDFN">Formalism 11 (first-order-logic)</a></div>
+<ol>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-141-Frame" class="MathJax"><nobr><span id="MathJax-Span-3653" class="math"><span style="display: inline-block; position: relative; width: 88px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3654" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3655" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3657" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3658" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3659" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3662" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-141" type="math/tex">W,\rho \models True</script> always holds.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-142-Frame" class="MathJax"><nobr><span id="MathJax-Span-3663" class="math"><span style="display: inline-block; position: relative; width: 93px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3664" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3665" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3666" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3667" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3668" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3669" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3670" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3671" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3672" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3673" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-142" type="math/tex">W,\rho \models False</script> never holds.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-143-Frame" class="MathJax"><nobr><span id="MathJax-Span-3674" class="math"><span style="display: inline-block; position: relative; width: 76px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3675" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3676" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3677" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3678" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3679" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3680" class="mi">¬</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3681" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-143" type="math/tex">W,\rho \models \neg \phi</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-144-Frame" class="MathJax"><nobr><span id="MathJax-Span-3682" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3683" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3684" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3685" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3686" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3687" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3688" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-144" type="math/tex">W,\rho \models
+ \phi</script> does not hold.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-145-Frame" class="MathJax"><nobr><span id="MathJax-Span-3689" class="math"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3690" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3691" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3693" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3694" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3695" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3696" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3697" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-145" type="math/tex">W,\rho \models \phi \wedge \psi</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-146-Frame" class="MathJax"><nobr><span id="MathJax-Span-3698" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3699" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3700" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3701" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3702" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3703" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3704" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-146" type="math/tex">W,\rho \models
+ \phi</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-147-Frame" class="MathJax"><nobr><span id="MathJax-Span-3705" class="math"><span style="display: inline-block; position: relative; width: 62px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3706" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3707" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3708" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3709" class="mi">i</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3710" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3711" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-147" type="math/tex">W,i\models \psi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-148-Frame" class="MathJax"><nobr><span id="MathJax-Span-3712" class="math"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3713" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3714" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3715" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3716" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3717" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3718" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3719" class="mo">∨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-3720" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-148" type="math/tex">W,\rho \models \phi \vee \psi</script> holds if either <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-149-Frame" class="MathJax"><nobr><span id="MathJax-Span-3721" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3722" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3723" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3724" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3725" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3726" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3727" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-149" type="math/tex">W,\rho \models \phi</script>
+ or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-150-Frame" class="MathJax"><nobr><span id="MathJax-Span-3728" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3729" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3730" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3731" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3732" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3733" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3734" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-150" type="math/tex">W,\rho \models \psi</script> holds.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-151-Frame" class="MathJax"><nobr><span id="MathJax-Span-3735" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3737" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3738" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3739" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3740" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3741" class="mi">ϕ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3742" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3743" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-151" type="math/tex">W,\rho \models \phi \Rightarrow \psi</script> holds if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-152-Frame" class="MathJax"><nobr><span id="MathJax-Span-3744" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3745" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3746" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3747" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3748" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3749" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3750" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-152" type="math/tex">W,\rho \models \phi</script>
+ implies <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-153-Frame" class="MathJax"><nobr><span id="MathJax-Span-3751" class="math"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3752" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3753" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3754" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3755" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3756" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3757" class="mi">ψ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.084em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.053em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-153" type="math/tex">W,\rho \models \psi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-154-Frame" class="MathJax"><nobr><span id="MathJax-Span-3758" class="math"><span style="display: inline-block; position: relative; width: 90px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3759" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3760" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3761" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3762" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3763" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3764" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3765" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3766" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3767" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-154" type="math/tex">W,\rho \models \exists x. \phi</script> holds if there exists some <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-155-Frame" class="MathJax"><nobr><span id="MathJax-Span-3768" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3769" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3770" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3771" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3772" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3773" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3774" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3775" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3776" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3778" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3780" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-155" type="math/tex">obj \in
+ Objects</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-156-Frame" class="MathJax"><nobr><span id="MathJax-Span-3781" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3782" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3783" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3785" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3786" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3787" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3788" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3789" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3790" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3791" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3792" class="mo">]</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3793" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3794" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-156" type="math/tex">W,\rho[x:=obj] \models \phi</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-157-Frame" class="MathJax"><nobr><span id="MathJax-Span-3795" class="math"><span style="display: inline-block; position: relative; width: 90px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3796" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3797" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3798" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3799" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3800" class="mo">⊨</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3801" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3802" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3803" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3804" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-157" type="math/tex">W,\rho \models \forall x. \phi</script> holds if there for every <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-158-Frame" class="MathJax"><nobr><span id="MathJax-Span-3805" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3806" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3807" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3808" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3809" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3810" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3811" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3812" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3813" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3814" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3815" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3817" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-158" type="math/tex">obj \in
+ Objects</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-159-Frame" class="MathJax"><nobr><span id="MathJax-Span-3818" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3819" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3820" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3821" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3822" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3823" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3824" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3825" class="mo">:<span style="font-family: STIXGeneral; font-style: normal; font-weight: normal;">=</span></span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3826" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3827" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3828" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3829" class="mo">]</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3830" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3831" class="mi">ϕ</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-159" type="math/tex">W,\rho[x:=obj] \models \phi</script>.</li>
+ </ol></div>
+
+<div class="remark">
+ <p>In the semantics above, note that the domain of quantification is
+ the set of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-160-Frame" class="MathJax"><nobr><span id="MathJax-Span-3832" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3833" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3834" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3835" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3836" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3837" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3838" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3840" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-160" type="math/tex">Objects</script>; that is, quantifiers range over entities,
+ activities, agents, or interactions (which are in turn further
+ subdivided into types of interactions). <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-161-Frame" class="MathJax"><nobr><span id="MathJax-Span-3841" class="math"><span style="display: inline-block; position: relative; width: 48px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.467em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3842" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3843" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3844" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3845" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3846" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3847" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3848" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-161" type="math/tex">Things</script> and relations
+ cannot be referenced directly by identifiers.
+</p>
+ </div>
+
+ <div class="remark">
+ <p>A PROV instance <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-162-Frame" class="MathJax"><nobr><span id="MathJax-Span-3849" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3850" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3851" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-162" type="math/tex">I</script> consists of a set of statements, each of
+ which can be translated to an atomic formula following the
+ definitional rules in PROV-CONSTRAINTS, possibly by introducing
+ fresh existential variables. Thus, we can view an
+ instance <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-163-Frame" class="MathJax"><nobr><span id="MathJax-Span-3852" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3853" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3854" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-163" type="math/tex">I</script> as a set of atomic formulas <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-164-Frame" class="MathJax"><nobr><span id="MathJax-Span-3855" class="math"><span style="display: inline-block; position: relative; width: 84px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.992em, -0.426em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3856" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3857" class="mo">{</span><span id="MathJax-Span-3858" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3859" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3860" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3861" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3862" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3863" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3864" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3865" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3866" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3867" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.12em; vertical-align: -0.326em;"></span></span></nobr></span><script id="MathJax-Element-164" type="math/tex">\{\phi_1,\ldots,\phi_n\}</script>, or equivalently a
+ single formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-165-Frame" class="MathJax"><nobr><span id="MathJax-Span-3868" class="math"><span style="display: inline-block; position: relative; width: 176px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.992em, -0.453em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3869" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3870" class="mi">∃</span><span id="MathJax-Span-3871" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3872" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3873" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3874" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3875" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3876" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3877" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3878" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3879" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3880" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3881" class="mtext"> </span><span id="MathJax-Span-3882" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3883" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3884" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3885" class="mo">∧</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3886" class="mo">⋯</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-3887" class="mo">∧</span><span style="padding-left: 0.25em;" id="MathJax-Span-3888" class="msubsup"><span style="display: inline-block; position: relative; width: 1.068em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.499em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3889" class="mi">ϕ</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.862em; left: 0.643em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3890" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.12em; vertical-align: -0.326em;"></span></span></nobr></span><script id="MathJax-Element-165" type="math/tex">\exists x_1,\ldots,x_k.~\phi_1 \wedge \cdots
+ \wedge \phi_n</script>, where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-166-Frame" class="MathJax"><nobr><span id="MathJax-Span-3891" class="math"><span style="display: inline-block; position: relative; width: 64px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.903em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3892" class="mrow"><span id="MathJax-Span-3893" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3894" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3895" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3896" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3897" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3898" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-3899" class="msubsup"><span style="display: inline-block; position: relative; width: 0.89em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3900" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.464em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3901" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.766em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-166" type="math/tex">x_1,\ldots,x_k</script> are the existential
+ variables of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-167-Frame" class="MathJax"><nobr><span id="MathJax-Span-3902" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3904" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-167" type="math/tex">I</script>.
+ </p>
+ </div>
+
+</section>
+ <section id="attribute-matching">
+
+<h3><span class="secno">4.2 </span> Attribute matching </h3>
+
+
+<p>We say that an object <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-168-Frame" class="MathJax"><nobr><span id="MathJax-Span-3905" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3906" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3907" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3908" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3909" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-168" type="math/tex">obj</script> matches attributes <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-169-Frame" class="MathJax"><nobr><span id="MathJax-Span-3910" class="math"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.901em, -0.438em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3911" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-3912" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3913" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3914" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3915" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3916" class="msubsup"><span style="display: inline-block; position: relative; width: 0.811em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3917" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3918" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3919" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3920" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3921" class="mi">a</span><span id="MathJax-Span-3922" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3923" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-3924" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3925" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3926" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3927" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3928" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-3929" class="mo">]</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.023em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-169" type="math/tex">[attr_1=val_1,...]</script> in structure <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-170-Frame" class="MathJax"><nobr><span id="MathJax-Span-3930" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3931" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3932" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.843em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-170" type="math/tex">W</script> provided:
+for each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-171-Frame" class="MathJax"><nobr><span id="MathJax-Span-3933" class="math"><span style="display: inline-block; position: relative; width: 30px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.903em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3934" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3935" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3936" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3938" class="msubsup"><span style="display: inline-block; position: relative; width: 0.636em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3939" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3940" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.878em; vertical-align: -0.231em;"></span></span></nobr></span><script id="MathJax-Element-171" type="math/tex">attr_i</script>, we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-172-Frame" class="MathJax"><nobr><span id="MathJax-Span-3941" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3942" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3943" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3944" class="mi">a</span><span id="MathJax-Span-3945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.541em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3946" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3947" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-3948" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-3949" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3950" class="mo">.</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3951" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3952" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3953" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3954" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3955" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3956" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3957" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3958" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3959" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3961" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3962" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3963" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span id="MathJax-Span-3964" class="msubsup"><span style="display: inline-block; position: relative; width: 0.636em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3965" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.386em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3966" class="mi">i</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3967" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-172" type="math/tex">val_i \in W.value(obj,attr_i)</script>.
+This is sometimes abbreviated as: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-173-Frame" class="MathJax"><nobr><span id="MathJax-Span-3968" class="math"><span style="display: inline-block; position: relative; width: 138px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3969" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3970" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3971" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3972" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3973" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3974" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3975" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3976" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3977" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3978" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3979" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3980" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3981" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-3982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3984" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3986" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3987" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-173" type="math/tex">match(W,obj,attrs)</script>.
+</p>
+
+</section>
+
+<section id="semantics-of-element-formulas">
+<h3><span class="secno">4.3 </span> Semantics of Element Formulas </h3>
+
+<section id="entity">
+
+<h4><span class="secno">4.3.1 </span> Entity </h4>
+
+<p>An entity formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-174-Frame" class="MathJax"><nobr><span id="MathJax-Span-3988" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-3989" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3990" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3991" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3994" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3995" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-3996" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3997" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-3998" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-3999" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4000" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4001" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4002" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4003" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4004" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4005" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-174" type="math/tex">entity(id,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-175-Frame" class="MathJax"><nobr><span id="MathJax-Span-4006" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4007" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4008" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4009" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-175" type="math/tex">id</script> denotes an entity.
+</p>
+<p>Entity formulas <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-176-Frame" class="MathJax"><nobr><span id="MathJax-Span-4010" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4011" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4012" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4013" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4017" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4018" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4019" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4020" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4023" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4025" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4026" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4027" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-176" type="math/tex">entity(id,attrs)</script> can be interpreted as follows:
+</p>
+<div data-title="Formalism 12 (rule_12)" data-count="12" id="rule_12" class="formalism"><div class="ruleTitle"><a href="#rule_12" class="internalDFN">Formalism 12 (rule_12)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-177-Frame" class="MathJax"><nobr><span id="MathJax-Span-4028" class="math"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4029" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4030" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4031" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4032" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4033" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4034" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4035" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4036" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4037" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4039" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4040" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4042" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4043" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4044" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4046" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4047" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4048" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4049" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-177" type="math/tex">W,\rho \models entity(id,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-178-Frame" class="MathJax"><nobr><span id="MathJax-Span-4050" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4051" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4052" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4053" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-178" type="math/tex">id</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-179-Frame" class="MathJax"><nobr><span id="MathJax-Span-4054" class="math"><span style="display: inline-block; position: relative; width: 153px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4055" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4056" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4057" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4058" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4059" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4060" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4061" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4062" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4063" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4064" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4065" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4066" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4067" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4068" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4069" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4070" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4073" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-179" type="math/tex">ent = \rho(id) \in Entities</script>
+</li>
+<li>the attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-180-Frame" class="MathJax"><nobr><span id="MathJax-Span-4074" class="math"><span style="display: inline-block; position: relative; width: 137px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4075" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4076" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4078" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4079" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4080" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4081" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4082" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4083" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4084" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4085" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4086" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4087" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4088" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4089" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4091" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4092" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4093" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-180" type="math/tex">match(W,ent, attrs)</script>.
+</li>
+</ol>
+
+
+</div>
+<div class="remark">
+<p>For example, the following formulas all hold if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-181-Frame" class="MathJax"><nobr><span id="MathJax-Span-4094" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4095" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4096" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-181" type="math/tex">x</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-182-Frame" class="MathJax"><nobr><span id="MathJax-Span-4097" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4098" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4099" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-182" type="math/tex">e</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-183-Frame" class="MathJax"><nobr><span id="MathJax-Span-4100" class="math"><span style="display: inline-block; position: relative; width: 256px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.707em, 1000em, 2.926em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4101" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4102" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4103" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4104" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4105" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4106" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4107" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4108" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4109" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4110" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4111" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4112" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4113" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4114" class="mn">4</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4115" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-4116" class="mn">5</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4117" class="mo">}</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4118" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4119" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4120" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4121" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4122" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4123" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4124" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4125" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4126" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4127" class="mi">b</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4128" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4129" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4130" class="mo">{</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4131" class="mn">6</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4132" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.055em; vertical-align: -0.256em;"></span></span></nobr></span><script id="MathJax-Element-183" type="math/tex">value(e,a) = \{4,5\}, value(e,b) = \{6\}</script> hold:
+</p><pre> entity(x,[])
+ entity(x,[a=5])
+ entity(x,[a=4,a=5])
+ entity(x,[a=4,b=6])
+</pre>
+<p>Note that PROV-CONSTRAINTS normalization will merge these formulas
+to a single one:
+</p>
+<pre> entity(x,[a=4,a=5,b=6])
+</pre>
+ </div>
+
+ </section>
+<section id="activity">
+
+<h4><span class="secno">4.3.2 </span> Activity </h4>
+
+<p>An activity formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-184-Frame" class="MathJax"><nobr><span id="MathJax-Span-4133" class="math"><span style="display: inline-block; position: relative; width: 155px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4134" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4135" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4136" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4137" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4138" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4139" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4140" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4141" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4142" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4143" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4144" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4145" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4146" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4147" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4149" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4150" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4152" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4153" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4154" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4155" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4156" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4157" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4158" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-184" type="math/tex">activity(id,st,et,attrs)</script>
+where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-185-Frame" class="MathJax"><nobr><span id="MathJax-Span-4159" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4160" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4161" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4162" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-185" type="math/tex">id</script> is a identifier referring to the activity, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-186-Frame" class="MathJax"><nobr><span id="MathJax-Span-4163" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4164" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4165" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4166" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-186" type="math/tex">st</script> is a start
+time and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-187-Frame" class="MathJax"><nobr><span id="MathJax-Span-4167" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4168" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4169" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-187" type="math/tex">et</script> is an end time, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-188-Frame" class="MathJax"><nobr><span id="MathJax-Span-4171" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4172" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4175" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4176" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4177" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-188" type="math/tex">attrs</script> are the attributes of
+activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-189-Frame" class="MathJax"><nobr><span id="MathJax-Span-4178" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4179" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4180" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4181" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-189" type="math/tex">id</script>.
+</p>
+<div data-title="Formalism 13 (rule_13)" data-count="13" id="rule_13" class="formalism"><div class="ruleTitle"><a href="#rule_13" class="internalDFN">Formalism 13 (rule_13)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-190-Frame" class="MathJax"><nobr><span id="MathJax-Span-4182" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4183" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4184" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4185" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4186" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4187" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4188" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4189" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4190" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4191" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4192" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4193" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4195" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4196" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4197" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4198" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4199" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4200" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4202" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4203" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4204" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4205" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4209" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4210" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4211" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-190" type="math/tex">W,\rho \models activity(id,st,et,attrs)</script>
+ holds if and only if:</p>
+<ol>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-191-Frame" class="MathJax"><nobr><span id="MathJax-Span-4212" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4213" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4214" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4215" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-191" type="math/tex">id</script> maps to an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-192-Frame" class="MathJax"><nobr><span id="MathJax-Span-4216" class="math"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4217" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4218" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4219" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4220" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4221" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4222" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4223" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4224" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4225" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4226" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4227" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4228" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4229" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4230" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4232" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4233" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4237" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-192" type="math/tex">act = \rho(id) \in Activities</script>
+</li>
+<li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-193-Frame" class="MathJax"><nobr><span id="MathJax-Span-4238" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4239" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4240" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4241" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-193" type="math/tex">st</script> is specified then it is equal to the start time of the activity, that is: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-194-Frame" class="MathJax"><nobr><span id="MathJax-Span-4242" class="math"><span style="display: inline-block; position: relative; width: 150px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4243" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4244" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4246" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4247" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4248" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4250" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4251" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4252" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4253" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4254" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4255" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4256" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4257" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4258" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4259" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4260" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4261" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4262" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-194" type="math/tex">min(lifetime(id)) = st</script>
+</li>
+<li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-195-Frame" class="MathJax"><nobr><span id="MathJax-Span-4264" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4265" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4266" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4267" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-195" type="math/tex">et</script> is specified then it is equal to the end time of the activity, that is: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-196-Frame" class="MathJax"><nobr><span id="MathJax-Span-4268" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4269" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4270" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4272" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4273" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4274" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4275" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4276" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4277" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4279" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4280" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4281" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4282" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4283" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4284" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4285" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4286" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4287" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4288" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4289" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-196" type="math/tex">max(lifetime(id)) = et</script>
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-197-Frame" class="MathJax"><nobr><span id="MathJax-Span-4290" class="math"><span style="display: inline-block; position: relative; width: 137px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4291" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4292" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4293" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4294" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4295" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4296" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4297" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4298" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4300" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4301" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4302" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4303" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4304" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4306" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4307" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4308" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4309" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-197" type="math/tex">match(W,act,attrs)</script>.
+</li>
+</ol>
+</div>
+</section>
+<section id="agent">
+
+<h4><span class="secno">4.3.3 </span> Agent </h4>
+
+<p>An agent formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-198-Frame" class="MathJax"><nobr><span id="MathJax-Span-4310" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4311" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4315" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4317" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4318" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4319" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4320" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4321" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4324" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4325" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4326" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-198" type="math/tex">agent(id,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-199-Frame" class="MathJax"><nobr><span id="MathJax-Span-4327" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4328" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4329" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4330" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-199" type="math/tex">id</script> denotes the agent and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-200-Frame" class="MathJax"><nobr><span id="MathJax-Span-4331" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4332" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4335" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4336" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4337" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-200" type="math/tex">attrs</script> describes additional attributes.
+</p>
+<div data-title="Formalism 14 (rule_14)" data-count="14" id="rule_14" class="formalism"><div class="ruleTitle"><a href="#rule_14" class="internalDFN">Formalism 14 (rule_14)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-201-Frame" class="MathJax"><nobr><span id="MathJax-Span-4338" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4339" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4340" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4341" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4342" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4343" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4344" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4345" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4346" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4347" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4348" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4349" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4350" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4351" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4353" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4354" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4355" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4356" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4357" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4358" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-201" type="math/tex">W,\rho \models agent(id,attrs)</script> holds if and only if:
+ </p>
+ <ol>
+ <li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-202-Frame" class="MathJax"><nobr><span id="MathJax-Span-4359" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4360" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4361" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4362" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-202" type="math/tex">id</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-203-Frame" class="MathJax"><nobr><span id="MathJax-Span-4363" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4364" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4365" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4366" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4367" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4368" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4369" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4370" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4371" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4372" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4373" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4374" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4375" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4376" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4377" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4379" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-203" type="math/tex">ag = \rho(id) \in Agents</script>
+ </li>
+ <li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-204-Frame" class="MathJax"><nobr><span id="MathJax-Span-4380" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4381" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4382" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4384" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4385" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4386" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4387" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4388" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4389" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4391" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4392" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4394" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4395" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4396" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4397" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4398" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-204" type="math/tex">match(W,ag,attrs)</script>.
+ </li>
+ </ol>
+</div>
+</section>
+</section>
+
+<section id="semantics-of-relations">
+<h3><span class="secno">4.4 </span> Semantics of Relations </h3>
+
+
+<section id="generation">
+<h4><span class="secno">4.4.1 </span> Generation </h4>
+
+<p>The generation formula is of the form
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-205-Frame" class="MathJax"><nobr><span id="MathJax-Span-4399" class="math"><span style="display: inline-block; position: relative; width: 227px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4400" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4401" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4402" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4403" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4404" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4405" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4406" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4408" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4409" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4411" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4412" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4413" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4414" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4415" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4416" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4417" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4418" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4419" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4420" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4421" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4422" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4424" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4425" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4428" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4429" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4430" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-205" type="math/tex">wasGeneratedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-206-Frame" class="MathJax"><nobr><span id="MathJax-Span-4431" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4432" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4433" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4434" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-206" type="math/tex">id</script> is an event identifier,
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-207-Frame" class="MathJax"><nobr><span id="MathJax-Span-4435" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4436" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4437" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-207" type="math/tex">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-208-Frame" class="MathJax"><nobr><span id="MathJax-Span-4438" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4439" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4440" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-208" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-209-Frame" class="MathJax"><nobr><span id="MathJax-Span-4441" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4442" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4443" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4444" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4445" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4446" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4447" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-209" type="math/tex">attrs</script> is
+a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-210-Frame" class="MathJax"><nobr><span id="MathJax-Span-4448" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4449" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-210" type="math/tex">t</script> is a time.
+</p>
+<div data-title="Formalism 15 (rule_15)" data-count="15" id="rule_15" class="formalism"><div class="ruleTitle"><a href="#rule_15" class="internalDFN">Formalism 15 (rule_15)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-211-Frame" class="MathJax"><nobr><span id="MathJax-Span-4451" class="math"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4452" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4453" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4454" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4455" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4456" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4457" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4459" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4460" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4461" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4462" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4463" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4464" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4466" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4468" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4469" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4470" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4471" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4472" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4473" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4474" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4475" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4476" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4477" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4478" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4481" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4484" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4485" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4486" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-211" type="math/tex">W,\rho \models
+ wasGeneratedBy(id,e,a,t,attrs)</script> holds if and only if:
+</p><ol>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-212-Frame" class="MathJax"><nobr><span id="MathJax-Span-4487" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4488" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4489" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4490" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-212" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-213-Frame" class="MathJax"><nobr><span id="MathJax-Span-4491" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4492" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4493" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4494" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4495" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4496" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4497" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4498" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4499" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4500" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4501" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4502" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4503" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4504" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4505" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4506" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4507" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4508" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-213" type="math/tex">evt = \rho(id) \in Events</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-214-Frame" class="MathJax"><nobr><span id="MathJax-Span-4509" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4510" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4511" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-214" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-215-Frame" class="MathJax"><nobr><span id="MathJax-Span-4512" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4513" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4514" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4515" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4517" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4518" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4519" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4520" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4521" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4522" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4523" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4524" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4527" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4528" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4529" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4530" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-215" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-216-Frame" class="MathJax"><nobr><span id="MathJax-Span-4531" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4532" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4533" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-216" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-217-Frame" class="MathJax"><nobr><span id="MathJax-Span-4534" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4535" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4536" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4537" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4538" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4539" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4540" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4541" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4542" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4543" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4544" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4545" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4546" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4548" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4549" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4550" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4551" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4552" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4554" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-217" type="math/tex">act = \rho(a) \in Activities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-218-Frame" class="MathJax"><nobr><span id="MathJax-Span-4555" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4556" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4557" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4558" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4559" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-218" type="math/tex">evt</script> is involved in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-219-Frame" class="MathJax"><nobr><span id="MathJax-Span-4560" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4561" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4562" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4563" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-219" type="math/tex">act</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-220-Frame" class="MathJax"><nobr><span id="MathJax-Span-4565" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4566" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4567" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4569" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4570" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4571" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4572" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4573" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4575" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4576" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4577" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4578" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4579" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4580" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4582" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4583" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4584" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4585" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4586" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4587" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4589" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4591" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-220" type="math/tex">(evt,act) \in EventActivities</script>.
+</li>
+<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-221-Frame" class="MathJax"><nobr><span id="MathJax-Span-4592" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4593" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4595" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-221" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-222-Frame" class="MathJax"><nobr><span id="MathJax-Span-4597" class="math"><span style="display: inline-block; position: relative; width: 74px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4598" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4602" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4603" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4604" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4606" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4607" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4608" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-222" type="math/tex">generation</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-223-Frame" class="MathJax"><nobr><span id="MathJax-Span-4609" class="math"><span style="display: inline-block; position: relative; width: 157px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4610" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4612" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4613" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4614" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4615" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4616" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4617" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4619" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4620" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4621" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4622" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4623" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4625" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4626" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4628" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4629" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4630" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-223" type="math/tex">type(evt) = generation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-224-Frame" class="MathJax"><nobr><span id="MathJax-Span-4631" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4632" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4633" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4634" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-224" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-225-Frame" class="MathJax"><nobr><span id="MathJax-Span-4636" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4637" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4638" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-225" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-226-Frame" class="MathJax"><nobr><span id="MathJax-Span-4639" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4640" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4641" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4642" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4643" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4644" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4645" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4646" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4647" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4648" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4649" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4650" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4651" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-226" type="math/tex">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-227-Frame" class="MathJax"><nobr><span id="MathJax-Span-4652" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4654" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4655" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4656" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-227" type="math/tex">evt</script> generated <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-228-Frame" class="MathJax"><nobr><span id="MathJax-Span-4657" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4658" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4659" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4660" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-228" type="math/tex">ent</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-229-Frame" class="MathJax"><nobr><span id="MathJax-Span-4662" class="math"><span style="display: inline-block; position: relative; width: 156px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4663" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4664" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4665" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4666" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4668" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4670" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4672" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4673" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4674" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4675" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4676" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4677" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4678" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4680" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4681" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4682" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-229" type="math/tex">(evt,ent) \in Generated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-230-Frame" class="MathJax"><nobr><span id="MathJax-Span-4683" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4684" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4685" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4686" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4687" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4688" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4689" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4690" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4691" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4693" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4694" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4695" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4700" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4701" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4702" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-230" type="math/tex">match(W,evt,attrs)</script>.
+</li>
+</ol>
+</div>
+
+</section>
+<section id="use">
+<h4><span class="secno">4.4.2 </span> Use </h4>
+
+<p>The use formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-231-Frame" class="MathJax"><nobr><span id="MathJax-Span-4703" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4704" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4705" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4706" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4707" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4708" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4709" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4710" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4711" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4712" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4713" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4714" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4715" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4716" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4718" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4719" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4720" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4721" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4722" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4723" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4724" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-231" type="math/tex">used(id,a,e,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-232-Frame" class="MathJax"><nobr><span id="MathJax-Span-4725" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4726" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4727" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4728" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-232" type="math/tex">id</script> denotes an event, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-233-Frame" class="MathJax"><nobr><span id="MathJax-Span-4729" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4730" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4731" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-233" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-234-Frame" class="MathJax"><nobr><span id="MathJax-Span-4732" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4733" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4734" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-234" type="math/tex">e</script> is an object identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-235-Frame" class="MathJax"><nobr><span id="MathJax-Span-4735" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4737" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4739" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4740" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4741" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-235" type="math/tex">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-236-Frame" class="MathJax"><nobr><span id="MathJax-Span-4742" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4743" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-236" type="math/tex">t</script> is an optional time.
+</p>
+<div data-title="Formalism 16 (rule_16)" data-count="16" id="rule_16" class="formalism"><div class="ruleTitle"><a href="#rule_16" class="internalDFN">Formalism 16 (rule_16)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-237-Frame" class="MathJax"><nobr><span id="MathJax-Span-4745" class="math"><span style="display: inline-block; position: relative; width: 195px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4746" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4747" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4748" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4749" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4750" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4751" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4752" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4753" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4754" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4755" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4756" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4757" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4758" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4759" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4760" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4761" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4762" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4763" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4764" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4765" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4767" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4768" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4769" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4770" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-237" type="math/tex">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
+
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-238-Frame" class="MathJax"><nobr><span id="MathJax-Span-4771" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4772" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4773" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4774" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-238" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-239-Frame" class="MathJax"><nobr><span id="MathJax-Span-4775" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4776" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4778" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4780" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4781" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4782" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4783" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4784" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4785" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4786" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4787" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4788" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4789" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4790" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4792" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-239" type="math/tex">evt = \rho(id) \in Events</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-240-Frame" class="MathJax"><nobr><span id="MathJax-Span-4793" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4794" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4795" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-240" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-241-Frame" class="MathJax"><nobr><span id="MathJax-Span-4796" class="math"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4797" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4798" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4799" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4801" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4802" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4803" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4804" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4805" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4806" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4807" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4808" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4809" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4812" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4813" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4814" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4815" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4816" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4817" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-241" type="math/tex">act = \rho(id) \in Activities</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-242-Frame" class="MathJax"><nobr><span id="MathJax-Span-4818" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4819" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4820" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-242" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-243-Frame" class="MathJax"><nobr><span id="MathJax-Span-4821" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4822" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4823" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4826" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4827" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4829" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4830" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4831" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4832" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4833" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4834" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4835" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4837" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4838" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4839" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-243" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-244-Frame" class="MathJax"><nobr><span id="MathJax-Span-4840" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4841" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4842" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4843" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-244" type="math/tex">evt</script> is part of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-245-Frame" class="MathJax"><nobr><span id="MathJax-Span-4845" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4846" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4847" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4848" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4849" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-245" type="math/tex">act</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-246-Frame" class="MathJax"><nobr><span id="MathJax-Span-4850" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4851" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4852" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4854" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4856" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4857" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4858" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4859" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4860" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4861" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4862" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4863" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4865" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4866" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4867" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4868" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4869" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4870" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4871" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4872" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4873" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4875" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4876" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-246" type="math/tex">(evt,act) \in EventActivities</script>.
+</li>
+<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-247-Frame" class="MathJax"><nobr><span id="MathJax-Span-4877" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4878" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4879" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4880" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4881" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-247" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-248-Frame" class="MathJax"><nobr><span id="MathJax-Span-4882" class="math"><span style="display: inline-block; position: relative; width: 23px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4883" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4884" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4885" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4886" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-248" type="math/tex">use</script>, i.e., <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-249-Frame" class="MathJax"><nobr><span id="MathJax-Span-4887" class="math"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4888" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4890" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4891" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4892" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4893" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4895" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4896" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4897" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4898" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4899" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4900" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4901" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-249" type="math/tex">type(evt) = use</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-250-Frame" class="MathJax"><nobr><span id="MathJax-Span-4902" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4904" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4905" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4906" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-250" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-251-Frame" class="MathJax"><nobr><span id="MathJax-Span-4907" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4908" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4909" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-251" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-252-Frame" class="MathJax"><nobr><span id="MathJax-Span-4910" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4911" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4912" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4913" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4914" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4915" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4916" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4917" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4918" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4919" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4920" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4921" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4922" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-252" type="math/tex">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-253-Frame" class="MathJax"><nobr><span id="MathJax-Span-4923" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4924" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4925" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4926" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4927" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-253" type="math/tex">evt</script> used <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-254-Frame" class="MathJax"><nobr><span id="MathJax-Span-4928" class="math"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4929" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4930" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4931" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4932" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-254" type="math/tex">obj</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-255-Frame" class="MathJax"><nobr><span id="MathJax-Span-4933" class="math"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4934" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-4935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4936" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4937" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4939" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4940" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4941" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4942" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4943" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-4944" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-4945" class="mi">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.043em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4946" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4947" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4948" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-255" type="math/tex">(evt,ent) \in Used</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-256-Frame" class="MathJax"><nobr><span id="MathJax-Span-4949" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4950" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4951" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4952" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4954" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4955" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4956" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4957" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4958" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4959" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4960" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4961" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4962" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4963" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4965" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4966" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4967" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4968" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-256" type="math/tex">match(W,evt,attrs)</script>.
+</li></div>
+
+</section>
+<section id="invalidation">
+<h4><span class="secno">4.4.3 </span> Invalidation </h4>
+
+<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-257-Frame" class="MathJax"><nobr><span id="MathJax-Span-4969" class="math"><span style="display: inline-block; position: relative; width: 233px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-4970" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4971" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4972" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4973" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4974" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4975" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4976" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4977" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4978" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4979" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4980" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4981" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4982" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4983" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4984" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4985" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4986" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4987" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4988" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4989" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4991" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4992" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4993" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-4994" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-4996" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-4997" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-4999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5000" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5001" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5002" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-257" type="math/tex">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-258-Frame" class="MathJax"><nobr><span id="MathJax-Span-5003" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5004" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5005" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5006" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-258" type="math/tex">id</script> is an event identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-259-Frame" class="MathJax"><nobr><span id="MathJax-Span-5007" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5008" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5009" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-259" type="math/tex">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-260-Frame" class="MathJax"><nobr><span id="MathJax-Span-5010" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5011" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5012" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-260" type="math/tex">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-261-Frame" class="MathJax"><nobr><span id="MathJax-Span-5013" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5014" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5015" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5016" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5017" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5018" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5019" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-261" type="math/tex">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-262-Frame" class="MathJax"><nobr><span id="MathJax-Span-5020" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5021" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5022" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-262" type="math/tex">t</script> is an optional time.</p>
+
+<div data-title="Formalism 17 (rule_17)" data-count="17" id="rule_17" class="formalism"><div class="ruleTitle"><a href="#rule_17" class="internalDFN">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-263-Frame" class="MathJax"><nobr><span id="MathJax-Span-5023" class="math"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5024" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5025" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5026" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5027" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5028" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5029" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5032" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5033" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5034" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5035" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5036" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5037" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5038" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5039" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5041" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5042" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5043" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5044" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5045" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5046" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5047" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5048" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5049" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5050" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5051" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5052" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5053" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5054" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5055" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5056" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5057" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5058" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5059" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5060" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-263" type="math/tex">W,\rho \models
+ wasInvalidatedBy(id,e,a,t,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-264-Frame" class="MathJax"><nobr><span id="MathJax-Span-5061" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5062" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5064" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-264" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-265-Frame" class="MathJax"><nobr><span id="MathJax-Span-5065" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5066" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5067" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5068" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5069" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5070" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5071" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5072" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5073" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5074" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5075" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5076" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5077" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5078" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5079" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5080" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5081" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5082" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-265" type="math/tex">evt = \rho(id) \in Events</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-266-Frame" class="MathJax"><nobr><span id="MathJax-Span-5083" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5084" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5085" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-266" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-267-Frame" class="MathJax"><nobr><span id="MathJax-Span-5086" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5087" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5088" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5089" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5091" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5092" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5093" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5094" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5095" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5096" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5097" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5098" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5099" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5100" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5101" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5102" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5103" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5104" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-267" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-268-Frame" class="MathJax"><nobr><span id="MathJax-Span-5105" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5106" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5107" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-268" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-269-Frame" class="MathJax"><nobr><span id="MathJax-Span-5108" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5109" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5110" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5111" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5112" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5113" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5114" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5115" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5116" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5117" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5118" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5119" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5120" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5121" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5122" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5123" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5124" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5125" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5126" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5127" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5128" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-269" type="math/tex">act = \rho(a) \in Activities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-270-Frame" class="MathJax"><nobr><span id="MathJax-Span-5129" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5130" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5131" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5132" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-270" type="math/tex">evt</script> is involved in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-271-Frame" class="MathJax"><nobr><span id="MathJax-Span-5134" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5135" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5136" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5137" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5138" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-271" type="math/tex">act</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-272-Frame" class="MathJax"><nobr><span id="MathJax-Span-5139" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5140" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5141" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5142" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5143" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5144" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5145" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5146" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5147" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5149" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5150" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5151" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5152" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5154" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5155" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5156" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5157" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5159" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5160" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5161" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5162" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5164" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5165" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-272" type="math/tex">(evt,act) \in EventActivities</script>.
+</li>
+<li>The type of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-273-Frame" class="MathJax"><nobr><span id="MathJax-Span-5166" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5168" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5169" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-273" type="math/tex">evt</script> is <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-274-Frame" class="MathJax"><nobr><span id="MathJax-Span-5171" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5172" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5173" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5174" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5175" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5176" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5177" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5178" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5179" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5180" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5181" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5182" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5183" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5184" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-274" type="math/tex">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-275-Frame" class="MathJax"><nobr><span id="MathJax-Span-5185" class="math"><span style="display: inline-block; position: relative; width: 166px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5186" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5187" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5188" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5189" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5190" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5191" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5193" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5195" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5196" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5197" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5198" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5199" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5200" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5201" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5202" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5203" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5204" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5205" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5206" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5207" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5208" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-275" type="math/tex">type(evt) = invalidation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-276-Frame" class="MathJax"><nobr><span id="MathJax-Span-5209" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5210" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5211" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5212" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-276" type="math/tex">evt</script> occurred at time <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-277-Frame" class="MathJax"><nobr><span id="MathJax-Span-5214" class="math"><span style="display: inline-block; position: relative; width: 5px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5215" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-277" type="math/tex">t</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-278-Frame" class="MathJax"><nobr><span id="MathJax-Span-5217" class="math"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5218" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5219" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5220" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5221" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5222" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5223" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5224" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5225" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5226" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5227" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5228" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-278" type="math/tex">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-279-Frame" class="MathJax"><nobr><span id="MathJax-Span-5230" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5231" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5232" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5233" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-279" type="math/tex">evt</script> invalidated <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-280-Frame" class="MathJax"><nobr><span id="MathJax-Span-5235" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5236" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5237" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5238" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5239" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-280" type="math/tex">ent</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-281-Frame" class="MathJax"><nobr><span id="MathJax-Span-5240" class="math"><span style="display: inline-block; position: relative; width: 163px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5241" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5242" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5243" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5244" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5248" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5250" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5251" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5252" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5253" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5254" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5255" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5256" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5257" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5258" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5259" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5260" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5261" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5262" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-281" type="math/tex">(evt,ent) \in Invalidated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-282-Frame" class="MathJax"><nobr><span id="MathJax-Span-5263" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5264" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5265" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5267" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5268" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5269" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5270" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5271" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5272" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5273" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5274" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5275" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5276" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5277" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5280" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5281" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5282" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-282" type="math/tex">match(W,evt,attrs)</script>.
+</li></ol></div>
+</section>
+
+<section id="association">
+
+<h4><span class="secno">4.4.4 </span> Association </h4>
+
+<p>An association formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-283-Frame" class="MathJax"><nobr><span id="MathJax-Span-5283" class="math"><span style="display: inline-block; position: relative; width: 262px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5284" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5285" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5287" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5288" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5290" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5291" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5292" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5296" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5297" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5298" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5299" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5300" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5301" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5302" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5303" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5304" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5305" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5306" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5307" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5309" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5310" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5311" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5312" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5313" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5317" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5318" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5319" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-283" type="math/tex">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
+
+<div data-title="Formalism 18 (rule_18)" data-count="18" id="rule_18" class="formalism"><div class="ruleTitle"><a href="#rule_18" class="internalDFN">Formalism 18 (rule_18)</a></div><p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-284-Frame" class="MathJax"><nobr><span id="MathJax-Span-5320" class="math"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5321" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5322" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5324" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5325" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5326" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5327" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5328" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5329" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5331" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5332" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5333" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5334" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5338" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5339" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5340" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5341" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5342" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5343" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5344" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5345" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5346" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5347" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5348" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5349" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5350" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5351" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5352" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5354" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5355" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5356" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5357" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5358" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5359" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5360" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-284" type="math/tex">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-285-Frame" class="MathJax"><nobr><span id="MathJax-Span-5361" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5362" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5364" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5365" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5366" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5367" class="mi">c</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-285" type="math/tex">assoc</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-286-Frame" class="MathJax"><nobr><span id="MathJax-Span-5368" class="math"><span style="display: inline-block; position: relative; width: 203px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5369" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5370" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5371" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5372" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5373" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5374" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5375" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5376" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5377" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5378" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5379" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5380" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5381" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5382" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5383" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5384" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5385" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5386" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5387" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5388" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5389" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5390" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5391" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5392" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5393" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-286" type="math/tex">assoc = \rho(id) \in Associations</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-287-Frame" class="MathJax"><nobr><span id="MathJax-Span-5394" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5395" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5396" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-287" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-288-Frame" class="MathJax"><nobr><span id="MathJax-Span-5397" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5398" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5399" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5400" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5401" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5402" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5403" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5404" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5405" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5406" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5407" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5408" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5409" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5411" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5412" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5413" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5415" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5416" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5417" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-288" type="math/tex">act = \rho(a) \in Activities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-289-Frame" class="MathJax"><nobr><span id="MathJax-Span-5418" class="math"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5419" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5420" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5421" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-289" type="math/tex">ag</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-290-Frame" class="MathJax"><nobr><span id="MathJax-Span-5422" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5423" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5425" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5426" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5427" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5429" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5430" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5431" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5432" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5433" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5434" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5435" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5436" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5437" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5438" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5439" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5441" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-290" type="math/tex">agent = \rho(ag) \in Agents</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-291-Frame" class="MathJax"><nobr><span id="MathJax-Span-5442" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5443" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5444" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5445" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-291" type="math/tex">pl</script> is either the placeholder <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-292-Frame" class="MathJax"><nobr><span id="MathJax-Span-5446" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5447" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5448" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-292" type="math/tex">-</script> or denotes a plan <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-293-Frame" class="MathJax"><nobr><span id="MathJax-Span-5449" class="math"><span style="display: inline-block; position: relative; width: 148px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5450" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5451" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5452" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5453" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5454" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5455" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5456" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5457" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5458" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5459" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5460" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5461" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5462" class="mi">P</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5463" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5464" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5465" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5466" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-293" type="math/tex">plan=\rho(pl) \in Plans</script>.
+</li>
+<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-294-Frame" class="MathJax"><nobr><span id="MathJax-Span-5467" class="math"><span style="display: inline-block; position: relative; width: 293px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5468" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5469" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5471" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5472" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5473" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5474" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5475" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5476" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5477" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5478" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5479" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5480" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5483" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5484" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5485" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5486" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5487" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5489" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5490" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5491" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5492" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5493" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5494" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5495" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5496" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5497" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5498" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5499" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5500" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5501" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5502" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5504" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5505" class="mi">h</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-294" type="math/tex">(assoc,agent,act,plan) \in AssociatedWith</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-295-Frame" class="MathJax"><nobr><span id="MathJax-Span-5506" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5507" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5508" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5509" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5511" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5512" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5513" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5514" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5515" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5516" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5517" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5518" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5519" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5520" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5521" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5522" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5523" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5525" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5526" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5527" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-295" type="math/tex">match(W,assoc,attrs)</script>.
+</li></ol></div>
+</section>
+<section id="start-formulas">
+<h4><span class="secno">4.4.5 </span> Start Formulas </h4>
+
+<p>A start formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-296-Frame" class="MathJax"><nobr><span id="MathJax-Span-5528" class="math"><span style="display: inline-block; position: relative; width: 223px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5529" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5530" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5531" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5532" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5533" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5535" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5536" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5538" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5539" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5540" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5541" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5542" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5543" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5544" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5545" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5546" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5547" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5548" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5549" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5550" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5551" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5552" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5553" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5554" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5555" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5557" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5559" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5560" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5561" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-296" type="math/tex">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+
+<div data-title="Formalism 19 (rule_19)" data-count="19" id="rule_19" class="formalism"><div class="ruleTitle"><a href="#rule_19" class="internalDFN">Formalism 19 (rule_19)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-297-Frame" class="MathJax"><nobr><span id="MathJax-Span-5562" class="math"><span style="display: inline-block; position: relative; width: 277px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5563" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5564" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5565" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5566" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5567" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5568" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5569" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5570" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5571" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5573" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5574" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5576" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5577" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5578" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5579" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5580" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5581" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5582" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5583" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5585" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5586" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5587" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5588" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5589" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5590" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5591" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5592" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5593" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5597" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5598" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5599" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-297" type="math/tex">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-298-Frame" class="MathJax"><nobr><span id="MathJax-Span-5600" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5601" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5602" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5603" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-298" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-299-Frame" class="MathJax"><nobr><span id="MathJax-Span-5604" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5605" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5606" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5607" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5608" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5609" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5610" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5611" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5612" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5613" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5614" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5615" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5616" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5617" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5618" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5619" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5620" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5621" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-299" type="math/tex">evt = \rho(id) \in Events</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-300-Frame" class="MathJax"><nobr><span id="MathJax-Span-5622" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5623" class="mrow"><span id="MathJax-Span-5624" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5625" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5626" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-300" type="math/tex">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-301-Frame" class="MathJax"><nobr><span id="MathJax-Span-5627" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5628" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5630" class="mi">c</span><span id="MathJax-Span-5631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5633" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5634" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5635" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5636" class="mo">(</span><span id="MathJax-Span-5637" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5638" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5639" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5640" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5641" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5642" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5643" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5645" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5646" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5647" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5648" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5649" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5651" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-301" type="math/tex">act_2 = \rho(a_2) \in Activities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-302-Frame" class="MathJax"><nobr><span id="MathJax-Span-5652" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5653" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5654" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-302" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-303-Frame" class="MathJax"><nobr><span id="MathJax-Span-5655" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5656" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5657" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5658" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5660" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5661" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5662" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5663" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5664" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5665" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5666" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5667" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5669" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5670" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5672" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5673" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-303" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-304-Frame" class="MathJax"><nobr><span id="MathJax-Span-5674" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5675" class="mrow"><span id="MathJax-Span-5676" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5677" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5678" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-304" type="math/tex">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-305-Frame" class="MathJax"><nobr><span id="MathJax-Span-5679" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5680" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5681" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5682" class="mi">c</span><span id="MathJax-Span-5683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5686" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5687" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5688" class="mo">(</span><span id="MathJax-Span-5689" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5690" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5691" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5692" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5693" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5694" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5695" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5697" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5698" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5699" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5700" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5701" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5702" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5703" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-305" type="math/tex">act_1 = \rho(a_1) \in Activities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-306-Frame" class="MathJax"><nobr><span id="MathJax-Span-5704" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5705" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5706" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5707" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-306" type="math/tex">evt</script> has type <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-307-Frame" class="MathJax"><nobr><span id="MathJax-Span-5709" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5710" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5711" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5713" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5715" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-307" type="math/tex">start</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-308-Frame" class="MathJax"><nobr><span id="MathJax-Span-5716" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5717" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5719" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5720" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5721" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5722" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5723" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5724" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5725" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5726" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5727" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5728" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5729" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5730" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5731" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5732" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-308" type="math/tex">type(evt) = start</script>.
+</li>
+<li>The event happened at the start of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-309-Frame" class="MathJax"><nobr><span id="MathJax-Span-5733" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5734" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5735" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5736" class="mi">c</span><span id="MathJax-Span-5737" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5739" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-309" type="math/tex">act_2</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-310-Frame" class="MathJax"><nobr><span id="MathJax-Span-5740" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5741" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5742" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5743" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5744" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5747" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5748" class="mi">c</span><span id="MathJax-Span-5749" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5750" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5751" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5752" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5753" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5754" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5755" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5757" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5758" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5759" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5760" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5761" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5762" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5764" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5765" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5767" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5768" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5769" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-310" type="math/tex">(evt,act_2)
+ \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-311-Frame" class="MathJax"><nobr><span id="MathJax-Span-5770" class="math"><span style="display: inline-block; position: relative; width: 214px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5771" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5772" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5773" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5774" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5775" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5776" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5778" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5779" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5780" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5781" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5782" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5783" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5784" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5785" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5786" class="mi">c</span><span id="MathJax-Span-5787" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5789" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5790" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5791" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5792" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5793" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5794" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5795" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5796" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5797" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5799" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5801" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-311" type="math/tex">min(lifetime(act_2)) = time(evt)</script>.
+</li>
+<li>TODO: The entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-312-Frame" class="MathJax"><nobr><span id="MathJax-Span-5802" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5803" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5804" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-312" type="math/tex">e</script> was generated by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-313-Frame" class="MathJax"><nobr><span id="MathJax-Span-5805" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5806" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5807" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5808" class="mi">c</span><span id="MathJax-Span-5809" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5811" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-313" type="math/tex">act_1</script> and started <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-314-Frame" class="MathJax"><nobr><span id="MathJax-Span-5812" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5813" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5814" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5815" class="mi">c</span><span id="MathJax-Span-5816" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5818" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-314" type="math/tex">act_2</script>.
+</li><li>The event happened during <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-315-Frame" class="MathJax"><nobr><span id="MathJax-Span-5819" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5820" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5822" class="mi">c</span><span id="MathJax-Span-5823" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5824" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5825" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-315" type="math/tex">act_1</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-316-Frame" class="MathJax"><nobr><span id="MathJax-Span-5826" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5827" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-5828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5829" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5830" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5832" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5833" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5834" class="mi">c</span><span id="MathJax-Span-5835" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5837" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5838" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5839" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5840" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5841" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5842" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5843" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5845" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5846" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5847" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5848" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5849" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5850" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5851" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5853" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5854" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5855" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-316" type="math/tex">(evt,act_1)
+ \in EventsActivities</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-317-Frame" class="MathJax"><nobr><span id="MathJax-Span-5856" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5857" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5858" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5861" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5862" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5863" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5864" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5865" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5866" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5867" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5869" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5870" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5871" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5872" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5873" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5874" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5875" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-317" type="math/tex">match(W,evt,attrs)</script>.
+</li></ol></div>
+</section>
+<section id="end">
+<h4><span class="secno">4.4.6 </span> End </h4>
+
+<p>An activity end formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-318-Frame" class="MathJax"><nobr><span id="MathJax-Span-5876" class="math"><span style="display: inline-block; position: relative; width: 217px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5877" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5878" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5879" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5880" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5881" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5882" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5883" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5884" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5885" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5886" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5887" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5888" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5889" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5890" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5891" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5892" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5893" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5894" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5895" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5896" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5897" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5898" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5899" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5900" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5901" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5902" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5905" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5906" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5907" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-318" type="math/tex">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+
+<div data-title="Formalism 20 (rule_20)" data-count="20" id="rule_20" class="formalism"><div class="ruleTitle"><a href="#rule_20" class="internalDFN">Formalism 20 (rule_20)</a></div>
+<p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-319-Frame" class="MathJax"><nobr><span id="MathJax-Span-5908" class="math"><span style="display: inline-block; position: relative; width: 271px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5909" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5910" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5911" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5912" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5913" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5914" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5916" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5917" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5918" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5919" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5920" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5921" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5922" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5923" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5924" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5925" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5926" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5927" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5928" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5929" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5930" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5931" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5932" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5933" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-5934" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5935" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5936" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5937" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-5938" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5939" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5941" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5942" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5943" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-319" type="math/tex">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</script> holds if and only
+ if:</p>
+
+<ol>
+ <li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-320-Frame" class="MathJax"><nobr><span id="MathJax-Span-5944" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5945" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5946" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5947" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-320" type="math/tex">id</script> denotes an event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-321-Frame" class="MathJax"><nobr><span id="MathJax-Span-5948" class="math"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5949" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5951" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5953" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5954" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5955" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5956" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5957" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5958" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5959" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5960" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5961" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5962" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5963" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5965" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-321" type="math/tex">evt = \rho(id) \in Events</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-322-Frame" class="MathJax"><nobr><span id="MathJax-Span-5966" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-5967" class="mrow"><span id="MathJax-Span-5968" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5969" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5970" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-322" type="math/tex">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-323-Frame" class="MathJax"><nobr><span id="MathJax-Span-5971" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5972" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5973" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5974" class="mi">c</span><span id="MathJax-Span-5975" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5976" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5977" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5978" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5979" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-5980" class="mo">(</span><span id="MathJax-Span-5981" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5982" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-5983" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-5984" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-5985" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-5986" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5987" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5989" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5990" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5991" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5994" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5995" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-323" type="math/tex">act_2 = \rho(a_2)\in Activities</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-324-Frame" class="MathJax"><nobr><span id="MathJax-Span-5996" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-5997" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-5998" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-324" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-325-Frame" class="MathJax"><nobr><span id="MathJax-Span-5999" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6000" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6001" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6002" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6003" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6004" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6005" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6006" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6007" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6008" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6009" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6010" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6011" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6012" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6013" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6016" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6017" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-325" type="math/tex">ent = \rho(e)\in Entities</script>.</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-326-Frame" class="MathJax"><nobr><span id="MathJax-Span-6018" class="math"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.509em); top: -2.044em; left: 0em;"><span id="MathJax-Span-6019" class="mrow"><span id="MathJax-Span-6020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6021" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6022" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-326" type="math/tex">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-327-Frame" class="MathJax"><nobr><span id="MathJax-Span-6023" class="math"><span style="display: inline-block; position: relative; width: 173px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6024" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6025" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6026" class="mi">c</span><span id="MathJax-Span-6027" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6029" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6030" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6031" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6032" class="mo">(</span><span id="MathJax-Span-6033" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6034" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6035" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6036" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6037" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6038" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6039" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6042" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6045" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6046" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6047" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-327" type="math/tex">act_1 = \rho(a_1)\in Activities</script>.</li>
+<li>The event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-328-Frame" class="MathJax"><nobr><span id="MathJax-Span-6048" class="math"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.763em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6049" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6050" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6051" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.728em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-328" type="math/tex">evt</script> has type <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-329-Frame" class="MathJax"><nobr><span id="MathJax-Span-6053" class="math"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6054" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6055" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6056" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6057" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-329" type="math/tex">end</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-330-Frame" class="MathJax"><nobr><span id="MathJax-Span-6058" class="math"><span style="display: inline-block; position: relative; width: 108px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6059" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6061" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6062" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6063" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6064" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6066" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6068" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6069" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6070" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6071" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6072" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-330" type="math/tex">type(evt) = end</script>.</li>
+<li>The event happened at the end of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-331-Frame" class="MathJax"><nobr><span id="MathJax-Span-6073" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6074" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6075" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6076" class="mi">c</span><span id="MathJax-Span-6077" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6078" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6079" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-331" type="math/tex">act_2</script>, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-332-Frame" class="MathJax"><nobr><span id="MathJax-Span-6080" class="math"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6081" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6082" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6083" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6084" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6085" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6086" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6087" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6088" class="mi">c</span><span id="MathJax-Span-6089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6090" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6091" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6092" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6093" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6094" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6095" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6096" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6097" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6098" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6099" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6100" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6101" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6102" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6103" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6104" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6105" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6106" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6107" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6108" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6109" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-332" type="math/tex">(evt,act_2)
+ \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-333-Frame" class="MathJax"><nobr><span id="MathJax-Span-6110" class="math"><span style="display: inline-block; position: relative; width: 217px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6111" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6112" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6113" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6114" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6115" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6116" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6117" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6118" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6119" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6122" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6123" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6124" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6125" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6126" class="mi">c</span><span id="MathJax-Span-6127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6129" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6130" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6131" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6132" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6134" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6135" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6136" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6137" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6138" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6139" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6141" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-333" type="math/tex">max(lifetime(act_2)) = time(evt)</script>.</li>
+ <li>TODO: The entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-334-Frame" class="MathJax"><nobr><span id="MathJax-Span-6142" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6143" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6144" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-334" type="math/tex">e</script> was generated by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-335-Frame" class="MathJax"><nobr><span id="MathJax-Span-6145" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6146" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6147" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6148" class="mi">c</span><span id="MathJax-Span-6149" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6150" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6151" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-335" type="math/tex">act_1</script> and ended <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-336-Frame" class="MathJax"><nobr><span id="MathJax-Span-6152" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6153" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6154" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6155" class="mi">c</span><span id="MathJax-Span-6156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6157" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6158" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-336" type="math/tex">act_2</script>.</li>
+
+<li>The event happened during <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-337-Frame" class="MathJax"><nobr><span id="MathJax-Span-6159" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6160" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6161" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6162" class="mi">c</span><span id="MathJax-Span-6163" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6164" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6165" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-337" type="math/tex">act_1</script>, that is, $(evt,act_1) \in EventActivities.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-338-Frame" class="MathJax"><nobr><span id="MathJax-Span-6166" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6167" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6168" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6169" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6171" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6172" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6173" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6174" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6175" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6176" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6177" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6178" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6179" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6180" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6181" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6182" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6183" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6184" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6185" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-338" type="math/tex">match(W,evt,attrs)</script>.</li>
+</ol>
+</div>
+</section>
+
+<section id="attribution">
+<h4><span class="secno">4.4.7 </span> Attribution </h4>
+
+<p>
+An attribution formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-339-Frame" class="MathJax"><nobr><span id="MathJax-Span-6186" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6187" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6188" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6189" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6190" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6191" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6192" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6194" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6195" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6196" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6197" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6199" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6200" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6201" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6202" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6203" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6204" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6205" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6206" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6207" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6208" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6209" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6210" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6211" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6212" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6215" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6216" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6217" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-339" type="math/tex">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
+</p>
+<div data-title="Formalism 21 (rule_21)" data-count="21" id="rule_21" class="formalism"><div class="ruleTitle"><a href="#rule_21" class="internalDFN">Formalism 21 (rule_21)</a></div>
+ <p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-340-Frame" class="MathJax"><nobr><span id="MathJax-Span-6218" class="math"><span style="display: inline-block; position: relative; width: 276px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6219" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6220" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6221" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6222" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6223" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6224" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6226" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6227" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6230" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6232" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6233" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6235" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6236" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6237" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6238" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6239" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6240" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6241" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6242" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6243" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6244" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6245" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6246" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6247" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6248" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6251" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6252" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6253" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-340" type="math/tex">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
+ holds if and only if:
+ </p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-341-Frame" class="MathJax"><nobr><span id="MathJax-Span-6254" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6255" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6256" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6257" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-341" type="math/tex">id</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-342-Frame" class="MathJax"><nobr><span id="MathJax-Span-6258" class="math"><span style="display: inline-block; position: relative; width: 203px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6259" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6261" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6262" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6263" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6264" class="mi">c</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6265" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6266" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6267" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6268" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6269" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6270" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6271" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6272" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6273" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6274" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6275" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6276" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6277" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6280" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6281" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6282" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6283" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-342" type="math/tex">assoc = \rho(id) \in Associations</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-343-Frame" class="MathJax"><nobr><span id="MathJax-Span-6284" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6285" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6286" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-343" type="math/tex">e</script> denotes an entity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-344-Frame" class="MathJax"><nobr><span id="MathJax-Span-6287" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6288" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6289" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6290" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6292" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6293" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6294" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6295" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6296" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6297" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6298" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6299" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6300" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6301" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6302" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6303" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6304" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6305" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-344" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-345-Frame" class="MathJax"><nobr><span id="MathJax-Span-6306" class="math"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6307" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6309" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-345" type="math/tex">ag</script> denotes an agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-346-Frame" class="MathJax"><nobr><span id="MathJax-Span-6310" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6311" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6315" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6316" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6317" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6318" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6319" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6321" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6322" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6323" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6324" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6325" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6326" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6327" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6328" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6329" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-346" type="math/tex">agent = \rho(ag) \in Agents</script>.
+</li>
+<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-347-Frame" class="MathJax"><nobr><span id="MathJax-Span-6330" class="math"><span style="display: inline-block; position: relative; width: 236px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6331" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6332" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6334" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6335" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6336" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6337" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6338" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6339" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6340" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6341" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6342" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6343" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6344" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6345" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6346" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6348" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6349" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6350" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6351" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6352" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6353" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6354" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6355" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6356" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6357" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6358" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6359" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6360" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6361" class="mi">o</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-347" type="math/tex">(assoc,ent,agent) \in AttributedTo</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-348-Frame" class="MathJax"><nobr><span id="MathJax-Span-6362" class="math"><span style="display: inline-block; position: relative; width: 136px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6363" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6364" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6365" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6367" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6368" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6369" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6370" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6371" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6372" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6373" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6376" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6377" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6379" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6380" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6381" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-348" type="math/tex">match(W,evt,attrs)</script>.
+</li></ol>
+</div>
+</section>
+
+<section id="communication">
+<h4><span class="secno">4.4.8 </span>Communication</h4>
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Communication</div></div>
+
+</section>
+
+
+<section id="responsibility">
+
+<h4><span class="secno">4.4.9 </span> Responsibility </h4>
+
+<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-349-Frame" class="MathJax"><nobr><span id="MathJax-Span-6382" class="math"><span style="display: inline-block; position: relative; width: 284px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6383" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6384" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6385" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6386" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6387" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6388" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6389" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6390" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6391" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6392" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6393" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6394" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6395" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6396" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6397" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6398" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6399" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6400" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6401" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6402" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6403" class="mi">a</span><span id="MathJax-Span-6404" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6405" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6406" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6407" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6408" class="mi">a</span><span id="MathJax-Span-6409" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6410" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6411" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6412" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6413" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6414" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6416" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6417" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6418" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6419" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6420" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6421" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6422" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-349" type="math/tex">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-350-Frame" class="MathJax"><nobr><span id="MathJax-Span-6423" class="math"><span style="display: inline-block; position: relative; width: 56px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.727em, 1000em, 2.758em, -0.577em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6424" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6425" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6426" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6428" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6429" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6430" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6431" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-350" type="math/tex">ActsFor</script> relation as follows:</p>
+
+<div data-title="Formalism 22 (rule_22)" data-count="22" id="rule_22" class="formalism"><div class="ruleTitle"><a href="#rule_22" class="internalDFN">Formalism 22 (rule_22)</a></div>
+ <p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-351-Frame" class="MathJax"><nobr><span id="MathJax-Span-6432" class="math"><span style="display: inline-block; position: relative; width: 338px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6433" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6434" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6435" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6436" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6437" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6439" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6441" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6442" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6443" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6444" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6445" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6446" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6447" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6449" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6450" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6451" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6452" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6453" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6454" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6455" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6456" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6457" class="mi">a</span><span id="MathJax-Span-6458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6459" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6460" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6462" class="mi">a</span><span id="MathJax-Span-6463" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6464" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6465" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6466" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6467" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6468" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6469" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6470" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6471" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6472" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6473" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6474" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6475" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6476" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-351" type="math/tex">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-352-Frame" class="MathJax"><nobr><span id="MathJax-Span-6477" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6478" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6479" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6480" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-352" type="math/tex">id</script> denotes an association <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-353-Frame" class="MathJax"><nobr><span id="MathJax-Span-6481" class="math"><span style="display: inline-block; position: relative; width: 199px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6482" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6483" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6485" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6486" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6487" class="mi">g</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6488" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6489" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6490" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6492" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6493" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6494" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6495" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6496" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6497" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6498" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6499" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6500" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6501" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6502" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6503" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6504" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6505" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-353" type="math/tex">deleg=\rho(id) \in Delegations</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-354-Frame" class="MathJax"><nobr><span id="MathJax-Span-6506" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6507" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6508" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-354" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-355-Frame" class="MathJax"><nobr><span id="MathJax-Span-6509" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6510" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6511" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6512" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6513" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6514" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6515" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6516" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6517" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6518" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6519" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6520" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6521" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6522" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6523" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6524" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6525" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6527" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6528" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6529" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-355" type="math/tex">act=\rho(a) \in Activities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-356-Frame" class="MathJax"><nobr><span id="MathJax-Span-6530" class="math"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6531" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6532" class="mi">a</span><span id="MathJax-Span-6533" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6534" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6535" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6537" class="mi">a</span><span id="MathJax-Span-6538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6539" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6540" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.855em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-356" type="math/tex">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-357-Frame" class="MathJax"><nobr><span id="MathJax-Span-6541" class="math"><span style="display: inline-block; position: relative; width: 299px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6542" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6544" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6545" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6546" class="mi">n</span><span id="MathJax-Span-6547" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6549" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6550" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6551" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6552" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6553" class="mi">a</span><span id="MathJax-Span-6554" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6555" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6556" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6557" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6558" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6560" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6561" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6562" class="mi">n</span><span id="MathJax-Span-6563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6565" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6566" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6567" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6568" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6569" class="mi">a</span><span id="MathJax-Span-6570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6571" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6572" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6573" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6574" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6575" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6576" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6577" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6578" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6579" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6580" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.107em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-357" type="math/tex">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
+</li>
+<li>The agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-358-Frame" class="MathJax"><nobr><span id="MathJax-Span-6581" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6582" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6583" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6584" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6585" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6586" class="mi">n</span><span id="MathJax-Span-6587" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6589" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-358" type="math/tex">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-359-Frame" class="MathJax"><nobr><span id="MathJax-Span-6590" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6591" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6592" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6593" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6595" class="mi">n</span><span id="MathJax-Span-6596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6598" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.93em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-359" type="math/tex">agent_1</script> with respect to the activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-360-Frame" class="MathJax"><nobr><span id="MathJax-Span-6599" class="math"><span style="display: inline-block; position: relative; width: 21px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6600" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6601" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6602" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-360" type="math/tex">act</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-361-Frame" class="MathJax"><nobr><span id="MathJax-Span-6604" class="math"><span style="display: inline-block; position: relative; width: 261px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6605" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-6606" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6607" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6608" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6609" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6610" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6611" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6612" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6613" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6614" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6615" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6616" class="mi">n</span><span id="MathJax-Span-6617" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6619" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6620" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6621" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6622" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6623" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6624" class="mi">n</span><span id="MathJax-Span-6625" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6626" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6627" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6628" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6630" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6632" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6633" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6634" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6635" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6637" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6638" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6639" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6640" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-361" type="math/tex">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-362-Frame" class="MathJax"><nobr><span id="MathJax-Span-6641" class="math"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6642" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6643" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6644" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6645" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6647" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6648" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6649" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6650" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6651" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6652" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6653" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6654" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6655" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6657" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6661" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6662" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-362" type="math/tex">match(W,assoc,attrs)</script>.
+</li></ol></div>
+</section>
+
+
+<section id="derivation">
+
+<h4><span class="secno">4.4.10 </span> Derivation </h4>
+
+<section id="precise">
+<h5><span class="secno">4.4.10.1 </span> Precise </h5>
+
+<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-363-Frame" class="MathJax"><nobr><span id="MathJax-Span-6663" class="math"><span style="display: inline-block; position: relative; width: 280px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6664" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6665" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6668" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6670" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6671" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6672" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6673" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6674" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6675" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6676" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6677" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6678" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6679" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6680" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6681" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6682" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6684" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6685" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6686" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6687" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6688" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6689" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6690" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6691" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6693" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6694" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6695" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6700" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6701" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6702" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-363" type="math/tex">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
+</p>
+<div data-title="Formalism 23 (rule_23)" data-count="23" id="rule_23" class="formalism"><div class="ruleTitle"><a href="#rule_23" class="internalDFN">Formalism 23 (rule_23)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-364-Frame" class="MathJax"><nobr><span id="MathJax-Span-6703" class="math"><span style="display: inline-block; position: relative; width: 347px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6704" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6705" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6706" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6707" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6708" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6709" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6710" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6711" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6712" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6713" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6715" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6716" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6717" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6718" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6719" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6720" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6721" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6722" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6723" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6724" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6725" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6726" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6727" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6728" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6729" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6733" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6735" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6736" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6737" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6738" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6739" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6740" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6741" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6742" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6743" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6746" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6747" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6748" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-364" type="math/tex">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-365-Frame" class="MathJax"><nobr><span id="MathJax-Span-6749" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6750" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6751" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6752" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-365" type="math/tex">id</script> denotes a derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-366-Frame" class="MathJax"><nobr><span id="MathJax-Span-6753" class="math"><span style="display: inline-block; position: relative; width: 196px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6754" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6755" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6757" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6758" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6759" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6760" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6761" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6762" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6764" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6765" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6766" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6767" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6768" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6769" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6771" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6772" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6773" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6774" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6775" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6776" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6777" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-366" type="math/tex">deriv = \rho(id) \in Derivations</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-367-Frame" class="MathJax"><nobr><span id="MathJax-Span-6778" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6779" class="mrow"><span id="MathJax-Span-6780" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6781" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6782" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6783" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-6784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6785" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6786" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-367" type="math/tex">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-368-Frame" class="MathJax"><nobr><span id="MathJax-Span-6787" class="math"><span style="display: inline-block; position: relative; width: 255px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6788" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6789" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6790" class="mi">n</span><span id="MathJax-Span-6791" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6792" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6793" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6794" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6795" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6796" class="mo">(</span><span id="MathJax-Span-6797" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6798" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6800" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6801" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6802" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6803" class="mi">n</span><span id="MathJax-Span-6804" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6805" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6806" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6807" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6808" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6809" class="mo">(</span><span id="MathJax-Span-6810" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6811" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6812" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6813" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6814" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6815" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6816" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6818" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6819" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6820" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6822" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-368" type="math/tex">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script> .
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-369-Frame" class="MathJax"><nobr><span id="MathJax-Span-6823" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6824" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6825" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-369" type="math/tex">a</script> denotes an activity <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-370-Frame" class="MathJax"><nobr><span id="MathJax-Span-6826" class="math"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6827" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6828" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6829" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6830" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6831" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6832" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6833" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6834" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6835" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6836" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6837" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6838" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6840" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6841" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6844" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6845" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6846" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-370" type="math/tex">act = \rho(a) \in Activities</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-371-Frame" class="MathJax"><nobr><span id="MathJax-Span-6847" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6848" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6849" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-371" type="math/tex">g</script> denotes a generation event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-372-Frame" class="MathJax"><nobr><span id="MathJax-Span-6850" class="math"><span style="display: inline-block; position: relative; width: 143px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6851" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6852" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6854" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6855" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6856" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6857" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6858" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6859" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6860" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6861" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6862" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6863" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6864" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6865" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6866" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-372" type="math/tex">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-373-Frame" class="MathJax"><nobr><span id="MathJax-Span-6867" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6868" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6869" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6870" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6871" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6872" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6873" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6874" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6875" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6876" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6877" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6878" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6879" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6880" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6881" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6882" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6883" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6884" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6885" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6886" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6887" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6888" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6889" class="mi">n</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-373" type="math/tex">type(\rho(g)) = generation</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-374-Frame" class="MathJax"><nobr><span id="MathJax-Span-6890" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6891" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6892" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-374" type="math/tex">u</script> denotes a use event <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-375-Frame" class="MathJax"><nobr><span id="MathJax-Span-6893" class="math"><span style="display: inline-block; position: relative; width: 97px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6894" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6895" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6896" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6897" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6898" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6899" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6900" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6901" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6902" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6903" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6905" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-375" type="math/tex">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-376-Frame" class="MathJax"><nobr><span id="MathJax-Span-6906" class="math"><span style="display: inline-block; position: relative; width: 114px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6907" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6908" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6909" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6910" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6911" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6912" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6913" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6914" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6915" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6916" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6917" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6918" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6919" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6920" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6921" class="mi">e</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-376" type="math/tex">type(\rho(u)) = use</script>.
+</li>
+<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-377-Frame" class="MathJax"><nobr><span id="MathJax-Span-6922" class="math"><span style="display: inline-block; position: relative; width: 339px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6923" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6924" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6925" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6926" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6927" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6928" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6929" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6930" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6931" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6933" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6934" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6936" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6939" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6940" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6941" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-6942" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-6943" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6944" class="mi">n</span><span id="MathJax-Span-6945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6946" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6947" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6948" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6949" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6951" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6952" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6953" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6954" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6955" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6956" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6957" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6958" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6959" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-6960" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-6961" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6962" class="mi">n</span><span id="MathJax-Span-6963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-6965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-377" type="math/tex">derivedFrom(deriv) =
+ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-378-Frame" class="MathJax"><nobr><span id="MathJax-Span-6966" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6967" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6968" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6971" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6972" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6973" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6974" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-6975" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6976" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6977" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6978" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6979" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6980" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6981" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-6982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6984" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6985" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6986" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-6987" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-378" type="math/tex">match(W,deriv,attrs)</script>.</li>
+</ol>
+</div>
+</section>
+<section id="imprecise">
+
+<h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
+<p>
+An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-379-Frame" class="MathJax"><nobr><span id="MathJax-Span-6988" class="math"><span style="display: inline-block; position: relative; width: 289px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-6989" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6990" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6991" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6992" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6993" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6994" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6995" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6996" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6997" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6998" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-6999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7000" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7001" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7002" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7003" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7004" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7005" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7006" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7007" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7008" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7009" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7010" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7011" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7012" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7013" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7014" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7015" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7016" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7017" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7018" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7019" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7020" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7023" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7025" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7026" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7027" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-379" type="math/tex">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
+
+<div data-title="Formalism 24 (rule_24)" data-count="24" id="rule_24" class="formalism"><div class="ruleTitle"><a href="#rule_24" class="internalDFN">Formalism 24 (rule_24)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-380-Frame" class="MathJax"><nobr><span id="MathJax-Span-7028" class="math"><span style="display: inline-block; position: relative; width: 343px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7029" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7030" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7031" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7032" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7033" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7034" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7035" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7036" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7037" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7038" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7039" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7040" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7041" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7042" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7043" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7044" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7045" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7046" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7047" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7048" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7049" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7050" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7054" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7058" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7059" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7060" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7061" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7062" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7063" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-7064" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7065" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7066" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7068" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7069" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7070" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7071" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-380" type="math/tex">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
+<ol>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-381-Frame" class="MathJax"><nobr><span id="MathJax-Span-7072" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7073" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7074" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7075" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-381" type="math/tex">id</script> denotes a derivation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-382-Frame" class="MathJax"><nobr><span id="MathJax-Span-7076" class="math"><span style="display: inline-block; position: relative; width: 196px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7077" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7078" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7079" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7080" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7082" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7083" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7084" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7085" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7086" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7087" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7088" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7089" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7090" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7091" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7092" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7093" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7094" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7095" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7096" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7097" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7098" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7099" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7100" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-382" type="math/tex">deriv = \rho(id) \in Derivations</script>
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-383-Frame" class="MathJax"><nobr><span id="MathJax-Span-7101" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7102" class="mrow"><span id="MathJax-Span-7103" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7104" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7105" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7106" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7109" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-383" type="math/tex">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-384-Frame" class="MathJax"><nobr><span id="MathJax-Span-7110" class="math"><span style="display: inline-block; position: relative; width: 255px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7111" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7112" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7113" class="mi">n</span><span id="MathJax-Span-7114" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7116" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7117" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7118" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7119" class="mo">(</span><span id="MathJax-Span-7120" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7121" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7122" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7123" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7124" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7125" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7126" class="mi">n</span><span id="MathJax-Span-7127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7129" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7130" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7131" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7132" class="mo">(</span><span id="MathJax-Span-7133" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7134" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7135" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7136" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7137" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7138" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7139" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7140" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7141" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7142" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7143" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7145" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-384" type="math/tex">ent_1 = \rho(e_1), ent_2=\rho(e_2) \in Entities</script>
+</li>
+<li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-385-Frame" class="MathJax"><nobr><span id="MathJax-Span-7146" class="math"><span style="display: inline-block; position: relative; width: 256px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7147" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7148" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7149" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7150" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7151" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7152" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7154" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7155" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7156" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7157" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7158" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7159" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7160" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7161" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7162" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7164" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7165" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7166" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7167" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7168" class="mi">n</span><span id="MathJax-Span-7169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7171" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-7172" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-7173" class="mi">w</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-7174" class="mo">⋅</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-7175" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7176" class="mi">n</span><span id="MathJax-Span-7177" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7178" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7179" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-385" type="math/tex">derivedFrom(deriv)= ent_2 \cdot w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-386-Frame" class="MathJax"><nobr><span id="MathJax-Span-7180" class="math"><span style="display: inline-block; position: relative; width: 11px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7181" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7182" class="mi">w</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.616em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-386" type="math/tex">w</script>
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-387-Frame" class="MathJax"><nobr><span id="MathJax-Span-7183" class="math"><span style="display: inline-block; position: relative; width: 151px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.514em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7184" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7185" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7187" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7188" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7189" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7190" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7191" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7192" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7193" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7194" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7195" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7196" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7197" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7198" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7199" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7200" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7202" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7203" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7204" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-387" type="math/tex">match(W,deriv,attrs)</script>.
+</li></ol></div>
+</section>
+</section>
+
+ <section id="influence">
+ <h4><span class="secno">4.4.11 </span>Influence</h4>
+
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO: Define influence semantics.</div></div>
+
+ </section>
+
+<section id="specialization">
+<h4><span class="secno">4.4.12 </span> Specialization </h4>
+
+<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-388-Frame" class="MathJax"><nobr><span id="MathJax-Span-7205" class="math"><span style="display: inline-block; position: relative; width: 165px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7206" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7207" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7208" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7209" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7210" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7211" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7212" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7213" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7214" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7215" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7216" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7217" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7218" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7219" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7220" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7221" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7222" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7223" class="mo">(</span><span id="MathJax-Span-7224" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7225" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7226" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7227" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7228" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7229" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7230" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7231" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-388" type="math/tex">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.
+</p>
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ <p>TODO: The content of this definition may be moved into the
+ structure W via an irreflexive/transitive specialization relation, since by
+ itself this definition is not transitive.</p>
+ </div></div>
+
+<div data-title="Formalism 25 (rule_25)" data-count="25" id="rule_25" class="formalism"><div class="ruleTitle"><a href="#rule_25" class="internalDFN">Formalism 25 (rule_25)</a></div> <p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-389-Frame" class="MathJax"><nobr><span id="MathJax-Span-7232" class="math"><span style="display: inline-block; position: relative; width: 219px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7233" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7234" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7235" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7236" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7237" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7238" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7239" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7240" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7241" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7242" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7246" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7247" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7250" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7251" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7252" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7253" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7254" class="mo">(</span><span id="MathJax-Span-7255" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7256" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7257" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7258" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7259" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7260" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7261" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7262" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-389" type="math/tex">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
+<ol>
+<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-390-Frame" class="MathJax"><nobr><span id="MathJax-Span-7263" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7264" class="mrow"><span id="MathJax-Span-7265" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7266" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7267" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-390" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-391-Frame" class="MathJax"><nobr><span id="MathJax-Span-7268" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7269" class="mrow"><span id="MathJax-Span-7270" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7271" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7272" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-391" type="math/tex">e_2</script> are entity identifiers, denoting
+ distinct entities <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-392-Frame" class="MathJax"><nobr><span id="MathJax-Span-7273" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7274" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7276" class="mi">n</span><span id="MathJax-Span-7277" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7278" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7279" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7280" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7281" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7282" class="mo">(</span><span id="MathJax-Span-7283" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7284" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7285" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7286" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7287" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7288" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7289" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7290" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7291" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7292" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7294" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7295" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-392" type="math/tex">ent_1
+ = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-393-Frame" class="MathJax"><nobr><span id="MathJax-Span-7296" class="math"><span style="display: inline-block; position: relative; width: 161px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7297" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7298" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7299" class="mi">n</span><span id="MathJax-Span-7300" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7301" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7302" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7303" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7304" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7305" class="mo">(</span><span id="MathJax-Span-7306" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7307" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7308" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7309" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7310" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7311" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7312" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7314" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7316" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7317" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7318" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-393" type="math/tex">ent_2 = \rho(e_2) \in Entities</script>,
+ where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-394-Frame" class="MathJax"><nobr><span id="MathJax-Span-7319" class="math"><span style="display: inline-block; position: relative; width: 79px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.901em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7320" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7321" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7322" class="mi">n</span><span id="MathJax-Span-7323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7324" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7326" class="mo">≠</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7327" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7328" class="mi">n</span><span id="MathJax-Span-7329" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7330" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7331" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-394" type="math/tex">ent_1 \neq ent_2</script>.
+</li>
+<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-395-Frame" class="MathJax"><nobr><span id="MathJax-Span-7332" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7333" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7335" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7337" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7338" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7339" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7340" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7341" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7342" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7343" class="mi">n</span><span id="MathJax-Span-7344" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7345" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7346" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7347" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7348" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7350" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7351" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7352" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7353" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7354" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7355" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7356" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7357" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7358" class="mi">n</span><span id="MathJax-Span-7359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7360" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7361" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7362" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-395" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>.
+</li>
+<li>The lifetime of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-396-Frame" class="MathJax"><nobr><span id="MathJax-Span-7363" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7364" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7365" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7366" class="mi">b</span><span id="MathJax-Span-7367" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7368" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7369" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-396" type="math/tex">obj_1</script> is contained in that of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-397-Frame" class="MathJax"><nobr><span id="MathJax-Span-7370" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7371" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7372" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7373" class="mi">n</span><span id="MathJax-Span-7374" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7376" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-397" type="math/tex">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-398-Frame" class="MathJax"><nobr><span id="MathJax-Span-7377" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7378" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7379" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7380" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7381" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7382" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7384" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7385" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7386" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7387" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7389" class="mi">n</span><span id="MathJax-Span-7390" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7392" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7393" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7394" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7395" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7396" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7397" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7398" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7400" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7401" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7402" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7403" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7404" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7405" class="mi">n</span><span id="MathJax-Span-7406" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7407" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7408" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7409" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-398" type="math/tex">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+</li>
+<li>For each attribute <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-399-Frame" class="MathJax"><nobr><span id="MathJax-Span-7410" class="math"><span style="display: inline-block; position: relative; width: 26px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7411" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7412" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7415" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.721em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-399" type="math/tex">attr</script> we have <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-400-Frame" class="MathJax"><nobr><span id="MathJax-Span-7416" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7417" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7418" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7419" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7420" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7421" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7422" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7423" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7424" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7425" class="mi">b</span><span id="MathJax-Span-7426" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7427" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7428" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7429" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7430" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7433" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7434" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7435" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7436" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7437" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7438" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7439" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7440" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7441" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7442" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7443" class="mi">b</span><span id="MathJax-Span-7444" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7445" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7446" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7447" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7451" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7452" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-400" type="math/tex">value(obj_1,attr) \supseteq value(obj_2,attr)</script>.
+</li></ol></div>
+
+<p>The second criterion says that the two Entities present aspects of
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-401-Frame" class="MathJax"><nobr><span id="MathJax-Span-7453" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7454" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7455" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7456" class="mi">b</span><span id="MathJax-Span-7457" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7458" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7459" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-401" type="math/tex">obj_1</script> and
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-402-Frame" class="MathJax"><nobr><span id="MathJax-Span-7460" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7461" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7462" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7463" class="mi">b</span><span id="MathJax-Span-7464" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7465" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7466" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-402" type="math/tex">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-403-Frame" class="MathJax"><nobr><span id="MathJax-Span-7467" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7468" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7469" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7470" class="mi">b</span><span id="MathJax-Span-7471" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7472" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7473" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-403" type="math/tex">obj_2</script> can be larger).
+The last criterion allows <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-404-Frame" class="MathJax"><nobr><span id="MathJax-Span-7474" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7475" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7476" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7477" class="mi">b</span><span id="MathJax-Span-7478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7479" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7480" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-404" type="math/tex">obj_1</script> to have more defined attributes than
+<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-405-Frame" class="MathJax"><nobr><span id="MathJax-Span-7481" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7482" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7483" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7484" class="mi">b</span><span id="MathJax-Span-7485" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7486" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7487" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-405" type="math/tex">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-406-Frame" class="MathJax"><nobr><span id="MathJax-Span-7488" class="math"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.499em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7489" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7490" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7491" class="mi">b</span><span id="MathJax-Span-7492" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7493" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7494" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-406" type="math/tex">obj_2</script>.
+</p>
+
+</section>
+<section id="alternate">
+
+<h4><span class="secno">4.4.13 </span> Alternate </h4>
+
+<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-407-Frame" class="MathJax"><nobr><span id="MathJax-Span-7495" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7496" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7497" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7498" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7499" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7500" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7501" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7502" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7504" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7505" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7506" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7507" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-407" type="math/tex">alternateOf</script> relation indicates when two entity formulas present (possibly different) aspects of the same thing. The two entities may or may not overlap in time.
+</p>
+<div data-title="Formalism 26 (rule_26)" data-count="26" id="rule_26" class="formalism"><div class="ruleTitle"><a href="#rule_26" class="internalDFN">Formalism 26 (rule_26)</a></div>
+ <p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-408-Frame" class="MathJax"><nobr><span id="MathJax-Span-7508" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7509" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7510" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7511" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7512" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7513" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7514" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7515" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7517" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7518" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7519" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7520" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7521" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7522" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7523" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7524" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7525" class="mo">(</span><span id="MathJax-Span-7526" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7527" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7528" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7529" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-7530" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7531" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7532" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7533" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-408" type="math/tex">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
+<ol>
+<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-409-Frame" class="MathJax"><nobr><span id="MathJax-Span-7534" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7535" class="mrow"><span id="MathJax-Span-7536" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7537" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7538" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-409" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-410-Frame" class="MathJax"><nobr><span id="MathJax-Span-7539" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7540" class="mrow"><span id="MathJax-Span-7541" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7542" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7543" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-410" type="math/tex">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-411-Frame" class="MathJax"><nobr><span id="MathJax-Span-7544" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7545" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7546" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7547" class="mi">n</span><span id="MathJax-Span-7548" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7550" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7551" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7552" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7553" class="mo">(</span><span id="MathJax-Span-7554" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7555" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7556" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7557" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-411" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-412-Frame" class="MathJax"><nobr><span id="MathJax-Span-7558" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7559" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7560" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7561" class="mi">n</span><span id="MathJax-Span-7562" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7563" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7564" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7565" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7566" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7567" class="mo">(</span><span id="MathJax-Span-7568" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7569" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7570" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7571" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-412" type="math/tex">ent_2 = \rho(e_2)</script>.
+</li>
+<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-413-Frame" class="MathJax"><nobr><span id="MathJax-Span-7572" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7573" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7575" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7576" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7577" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7578" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7579" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7580" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7581" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7582" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7583" class="mi">n</span><span id="MathJax-Span-7584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7585" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7586" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7587" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7588" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7589" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7590" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7591" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7592" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7593" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7594" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7595" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7596" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7597" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7598" class="mi">n</span><span id="MathJax-Span-7599" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7600" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7601" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7602" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-413" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>
+</li></ol>
+</div>
+
+
+</section>
+
+
+<section id="membership">
+
+<h4><span class="secno">4.4.14 </span> Membership </h4>
+
+<p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-414-Frame" class="MathJax"><nobr><span id="MathJax-Span-7603" class="math"><span style="display: inline-block; position: relative; width: 84px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.507em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7604" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7605" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7606" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7607" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7608" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7610" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7611" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7612" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7613" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-414" type="math/tex">hadMember</script> relation relates a collection to an element of the collection.
+</p>
+<div data-title="Formalism 27 (rule_27)" data-count="27" id="rule_27" class="formalism"><div class="ruleTitle"><a href="#rule_27" class="internalDFN">Formalism 27 (rule_27)</a></div>
+ <p>
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-415-Frame" class="MathJax"><nobr><span id="MathJax-Span-7614" class="math"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7615" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7616" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7617" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7618" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7619" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7620" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7621" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7622" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7623" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7625" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7626" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7628" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7629" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7630" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7631" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7632" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7633" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-415" type="math/tex">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
+<ol>
+<li>[WF] Both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-416-Frame" class="MathJax"><nobr><span id="MathJax-Span-7634" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7635" class="mrow"><span id="MathJax-Span-7636" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7637" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7638" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-416" type="math/tex">e_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-417-Frame" class="MathJax"><nobr><span id="MathJax-Span-7639" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-7640" class="mrow"><span id="MathJax-Span-7641" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7642" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-7643" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-417" type="math/tex">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-418-Frame" class="MathJax"><nobr><span id="MathJax-Span-7644" class="math"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.496em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7645" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7646" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7647" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7649" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7650" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7651" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7652" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7653" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7654" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7655" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7656" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7657" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7658" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7659" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7660" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7661" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7663" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7664" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7665" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7666" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-418" type="math/tex">coll
+ = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-419-Frame" class="MathJax"><nobr><span id="MathJax-Span-7667" class="math"><span style="display: inline-block; position: relative; width: 147px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7668" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7669" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7670" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7672" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7673" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7674" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7675" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7676" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7677" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7678" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7679" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7680" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7681" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7682" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7683" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7684" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7685" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-419" type="math/tex">ent = \rho(e) \in Entities</script>.
+</li>
+<li>TODO
+</li></ol>
+</div>
+<div class="note"><div class="note-title"><span>Note</span></div><div class="">
+ <p>Additional constraints needed above to refer to (not yet defined)
+collection structure of entities/things.</p>
+ </div></div>
+
+
+</section>
+
+</section>
+
+ <section id="auxiliary-formulas">
+ <h3><span class="secno">4.5 </span>Auxiliary formulas</h3>
+
+ <p>In this section, we define the semantics of additional formulas
+ concerning ordering, null values, and typing. These are used in the
+ logical versions of constraints.</p>
+
+ <section id="equals">
+ <h4><span class="secno">4.5.1 </span>Equals</h4>
+ <p>As usual, an equality formula means that two expressions denote
+ the same value. Identifiers always denote <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-420-Frame" class="MathJax"><nobr><span id="MathJax-Span-7686" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.466em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7687" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7688" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7689" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7690" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7691" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7692" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7693" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7694" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-420" type="math/tex">Objects</script>.</p>
+ <div data-title="Formalism 28 (equality)" data-count="28" class="formalism" id="equality"><div class="ruleTitle"><a href="#equality" class="internalDFN">Formalism 28 (equality)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-421-Frame" class="MathJax"><nobr><span id="MathJax-Span-7695" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7696" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7697" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7698" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7699" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7700" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7701" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7702" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7703" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-421" type="math/tex">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-422-Frame" class="MathJax"><nobr><span id="MathJax-Span-7704" class="math"><span style="display: inline-block; position: relative; width: 78px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7705" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7706" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7707" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7708" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7709" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7710" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7711" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7712" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7713" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7714" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-422" type="math/tex">\rho(x) =
+ \rho(y)</script>.</p>
+ </div>
+ </section>
+ <section id="precedes-and-strictly-precedes">
+ <h4><span class="secno">4.5.2 </span>Precedes and Strictly Precedes</h4>
+ <p>The precedes relation <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-423-Frame" class="MathJax"><nobr><span id="MathJax-Span-7715" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7716" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7717" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7718" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7719" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.997em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-423" type="math/tex">x \preceq y</script> holds between two events, one taking
+ place before (or simultaneously with) another. Since the
+ reference semantics assumes that times are linearly ordered and
+ event times are
+ mapped to a single time line, this amounts to
+ comparing the event times. The semantics of strictly precedes (<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-424-Frame" class="MathJax"><nobr><span id="MathJax-Span-7720" class="math"><span style="display: inline-block; position: relative; width: 38px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.863em, 1000em, 2.951em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7721" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7722" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7723" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7724" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.915em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-424" type="math/tex">x
+ \prec y</script> is similar, only <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-425-Frame" class="MathJax"><nobr><span id="MathJax-Span-7725" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7726" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7727" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-425" type="math/tex">x</script> must take place strictly before <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-426-Frame" class="MathJax"><nobr><span id="MathJax-Span-7728" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.55em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7729" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7730" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-426" type="math/tex">y</script>).</p>
+ <div data-title="Formalism 29 (precedes)" data-count="29" class="formalism" id="precedes"><div class="ruleTitle"><a href="#precedes" class="internalDFN">Formalism 29 (precedes)</a></div>
+ <ol>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-427-Frame" class="MathJax"><nobr><span id="MathJax-Span-7731" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7732" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7733" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7735" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7736" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7737" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7738" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7739" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-427" type="math/tex">W,\rho \models x \preceq y</script> holds if and only if
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-428-Frame" class="MathJax"><nobr><span id="MathJax-Span-7740" class="math"><span style="display: inline-block; position: relative; width: 131px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7741" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7742" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7743" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7744" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7745" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7747" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7748" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7749" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7750" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7751" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7752" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7753" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7754" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7755" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7756" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7757" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-428" type="math/tex">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-429-Frame" class="MathJax"><nobr><span id="MathJax-Span-7758" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7759" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7762" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7763" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7764" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7765" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7766" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7767" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7768" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7769" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7770" class="mo">≤</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7772" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7773" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7774" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7775" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7776" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7777" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7778" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7779" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7780" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-429" type="math/tex">time(\rho(x)) \leq time(\rho(y))</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-430-Frame" class="MathJax"><nobr><span id="MathJax-Span-7781" class="math"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7782" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7783" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7785" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7786" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7787" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7788" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7789" class="mi">y</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.054em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-430" type="math/tex">W,\rho \models x \prec y</script> holds if and only if
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-431-Frame" class="MathJax"><nobr><span id="MathJax-Span-7790" class="math"><span style="display: inline-block; position: relative; width: 131px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7791" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7792" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7793" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7794" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7795" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7796" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7797" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7798" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7799" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7800" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7801" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7802" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7803" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7804" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7805" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7807" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-431" type="math/tex">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-432-Frame" class="MathJax"><nobr><span id="MathJax-Span-7808" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7809" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7811" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7812" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7813" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7814" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7815" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7816" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7817" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7818" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7819" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7820" class="mo"><</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7822" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7823" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7824" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7825" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7826" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7827" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7828" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7829" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7830" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-432" type="math/tex">time(\rho(x)) < time(\rho(y))</script>.</li>
+ </ol>
+ </div>
+ </section>
+
+ <section id="notnull">
+ <h4><span class="secno">4.5.3 </span>notNull</h4>
+ <p>The <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-433-Frame" class="MathJax"><nobr><span id="MathJax-Span-7831" class="math"><span style="display: inline-block; position: relative; width: 72px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.512em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7832" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7833" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7834" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7836" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7837" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7838" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7839" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7840" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7841" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7842" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-433" type="math/tex">notNull(x)</script> formula is used to specify that a value may not
+ be the null value <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-434-Frame" class="MathJax"><nobr><span id="MathJax-Span-7843" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.745em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7844" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-7845" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.833em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-434" type="math/tex">\bot</script>. The symbol <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-435-Frame" class="MathJax"><nobr><span id="MathJax-Span-7846" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7847" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-7848" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-435" type="math/tex">-</script> always denotes the null
+ value (i.e. <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-436-Frame" class="MathJax"><nobr><span id="MathJax-Span-7849" class="math"><span style="display: inline-block; position: relative; width: 66px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7850" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7851" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7852" class="mo">(</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7853" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7854" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7855" class="mo">=</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7856" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-436" type="math/tex">\rho(-) = \bot</script>).
+ </p><div data-title="Formalism 30 (notNull)" data-count="30" class="formalism" id="notNull"><div class="ruleTitle"><a href="#notNull" class="internalDFN">Formalism 30 (notNull)</a></div>
+ <p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-437-Frame" class="MathJax"><nobr><span id="MathJax-Span-7857" class="math"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7858" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7859" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7860" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7861" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7862" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7863" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7864" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7865" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7866" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7867" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7868" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7869" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7870" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7871" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7872" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-437" type="math/tex">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-438-Frame" class="MathJax"><nobr><span id="MathJax-Span-7873" class="math"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.901em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7874" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7875" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7876" class="mo">≠</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7877" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1em; vertical-align: -0.229em;"></span></span></nobr></span><script id="MathJax-Element-438" type="math/tex">e \neq
+ \bot</script>.
+ </p>
+ </div>
+
+ </section>
+
+ <section id="typeof">
+ <h4><span class="secno">4.5.4 </span>typeOf</h4>
+
+ <p>The typing formula <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-439-Frame" class="MathJax"><nobr><span id="MathJax-Span-7878" class="math"><span style="display: inline-block; position: relative; width: 80px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7879" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7880" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7881" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7882" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7883" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7884" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7885" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7886" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7887" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7888" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7890" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-439" type="math/tex">typeOf(x,t)</script> constrains the type of the value of
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-440-Frame" class="MathJax"><nobr><span id="MathJax-Span-7891" class="math"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.553em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7892" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7893" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-440" type="math/tex">x</script>. </p>
+
+ <div data-title="Formalism 31 (typeOf)" data-count="31" class="formalism" id="typeOf"><div class="ruleTitle"><a href="#typeOf" class="internalDFN">Formalism 31 (typeOf)</a></div>
+ <ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-441-Frame" class="MathJax"><nobr><span id="MathJax-Span-7894" class="math"><span style="display: inline-block; position: relative; width: 168px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7895" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7896" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7897" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7898" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7899" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7900" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7901" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7902" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7903" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7904" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7905" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7906" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7907" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7908" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7909" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7910" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7911" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7912" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7914" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7915" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-441" type="math/tex">W,\rho\models typeOf(e,entity)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-442-Frame" class="MathJax"><nobr><span id="MathJax-Span-7916" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7917" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7918" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7919" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7920" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7921" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7922" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7923" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7924" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7925" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7926" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7927" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7928" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7929" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7930" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-442" type="math/tex">\rho(e) \in Entities</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-443-Frame" class="MathJax"><nobr><span id="MathJax-Span-7931" class="math"><span style="display: inline-block; position: relative; width: 181px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7932" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7933" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7934" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7935" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7936" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7938" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7939" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7940" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7941" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7942" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7943" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7944" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7945" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7946" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7947" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7949" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7950" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7951" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7953" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7954" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-443" type="math/tex">W,\rho\models typeOf(a,activity)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-444-Frame" class="MathJax"><nobr><span id="MathJax-Span-7955" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7956" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7957" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7958" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7959" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7960" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7961" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7962" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7963" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7964" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7965" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7966" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7967" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7968" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7969" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7970" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7971" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-444" type="math/tex">\rho(a) \in Activities</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-445-Frame" class="MathJax"><nobr><span id="MathJax-Span-7972" class="math"><span style="display: inline-block; position: relative; width: 176px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7973" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7974" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7975" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7976" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-7977" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-7978" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7979" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7980" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7981" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7982" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7983" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7984" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7985" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7986" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7987" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-7988" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7989" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7990" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7991" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-7993" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.072em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-445" type="math/tex">W,\rho\models typeOf(ag,agent)</script> holds if and only if
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-446-Frame" class="MathJax"><nobr><span id="MathJax-Span-7994" class="math"><span style="display: inline-block; position: relative; width: 105px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.566em); top: -2.57em; left: 0em;"><span id="MathJax-Span-7995" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7996" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-7997" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7998" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-7999" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8000" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8001" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8002" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8003" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8004" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8005" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8006" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8007" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-446" type="math/tex">\rho(ag) \in Agents</script>.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-447-Frame" class="MathJax"><nobr><span id="MathJax-Span-8008" class="math"><span style="display: inline-block; position: relative; width: 249px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8009" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8010" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8011" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8012" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8013" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8015" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8016" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8017" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8018" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8019" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8020" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8021" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8022" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8023" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8024" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8025" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8026" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8027" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8028" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8029" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8030" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8031" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8032" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8033" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8034" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8035" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8036" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8037" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8038" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-447" type="math/tex">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
+ TODO.</li>
+ <li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-448-Frame" class="MathJax"><nobr><span id="MathJax-Span-8039" class="math"><span style="display: inline-block; position: relative; width: 293px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8040" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8041" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8043" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8044" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8046" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8047" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8048" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8049" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8050" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8051" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8052" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8053" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8054" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8055" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8056" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8057" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8058" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-8059" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8060" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8061" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8063" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8064" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8065" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8066" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8067" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8069" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8070" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8072" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8073" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8074" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-448" type="math/tex">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
+ TODO.</li>
+ </ol>
+
+ </div>
+
+ <div class="note"><div class="note-title"><span>Note</span></div><div class="">TODO Collections</div></div>
+
+ </section>
+
+ </section>
+ </section>
+
+<section id="theory">
+<!--OddPage--><h2><span class="secno">5. </span> Inferences and Constraints </h2>
+
+ <p>
+ In this section we restate all of the inferences and constraints
+ of PROV-CONSTRAINTS in terms of first-order logic. For each, we
+ give a proof sketch showing why the inference or constraint is
+ sound for reasoning about the reference semantics. We exclude the
+ definitional rules in PROV-CONSTRAINTS because they are only
+ needed for expanding the abbreviated forms of PROV-N statements to
+ the logical formulas used here.</p>
+<section id="inferences">
+<h3><span class="secno">5.1 </span>Inferences</h3>
+
+<div class="inference" number="5" id="communication-generation-use-inference"><div class="ruleTitle"><a href="#communication-generation-use-inference" class="internalDFN">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-449-Frame" class="MathJax"><nobr><span id="MathJax-Span-8075" class="math"><span style="display: inline-block; position: relative; width: 573px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.049em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8076" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8077" class="mtable"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.502em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8078" class="mtd"><span id="MathJax-Span-8079" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8080" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8082" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8083" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8084" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8085" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8086" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8087" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8088" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8089" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8090" class="mn">1</span><span style="display: inline-block; 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padding-left: 0.188em;" id="MathJax-Span-8098" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8099" class="mtd"><span id="MathJax-Span-8100" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8101" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8102" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8103" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8104" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8105" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; 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top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8121" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8122" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8123" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8124" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8125" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8126" class="mo">,</span><span style="font-family: STIXGeneral; 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padding-left: 0.188em;" id="MathJax-Span-8186" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8187" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8188" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8189" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8190" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8191" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8192" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8193" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8194" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8195" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8196" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8197" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8198" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8199" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8200" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8201" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8202" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8203" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8204" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8205" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8207" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8208" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8209" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8210" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8211" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-449" type="math/tex">\begin{array}[t]{l}
+\forall id,a_2,a_1,attrs.~
+\\
+\qquad wasInformedBy(id,a_2,a_1,attrs)
+\\
+\quad\Rightarrow
+\exists e,gen,t_1,use,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge used(use,a_2,e,t_2,[])
+\end{array}</script></div>
+<div class="inference" number="6" id="generation-use-communication-inference"><div class="ruleTitle"><a href="#generation-use-communication-inference" class="internalDFN">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-450-Frame" class="MathJax"><nobr><span id="MathJax-Span-8212" class="math"><span style="display: inline-block; position: relative; width: 493px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8213" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8214" class="mtable"><span style="display: inline-block; position: relative; width: 28.446em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.446em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8215" class="mtd"><span id="MathJax-Span-8216" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8217" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8218" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8219" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8220" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8221" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8222" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8223" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8224" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8225" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8226" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8227" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8228" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8230" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8231" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8232" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8235" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8236" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8237" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8238" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8239" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8240" class="mi">i</span><span id="MathJax-Span-8241" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8243" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8244" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8245" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8246" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8247" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8248" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8249" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8251" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8252" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8253" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8255" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8256" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8257" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8258" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8259" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8260" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8261" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-8262" class="mtd"><span id="MathJax-Span-8263" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8264" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8265" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8267" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8268" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8269" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8270" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8271" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8272" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8273" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8274" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8275" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8276" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8277" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8278" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8279" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8280" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8281" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8282" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8283" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8284" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8285" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8286" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8287" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8288" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8289" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8290" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8292" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8297" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8298" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8299" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8300" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8301" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8302" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8303" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8304" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8305" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8306" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8307" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8308" class="mi">i</span><span id="MathJax-Span-8309" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8310" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8311" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8312" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8313" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8314" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8315" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8316" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8317" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8318" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8319" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8320" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8321" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8322" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8323" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8324" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8325" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8326" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-8327" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8328" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8329" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8330" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-8331" class="mtd"><span id="MathJax-Span-8332" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8333" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8334" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8335" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8338" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8339" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8340" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8341" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8342" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8343" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8344" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8345" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8346" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8347" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8348" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8349" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8350" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8351" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8352" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8353" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8354" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8355" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8356" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8357" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8358" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8359" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8362" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8364" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8365" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8366" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8367" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-450" type="math/tex">\begin{array}[t]{l}
+\forall gen,e,a_1,t_1,attrs_1,id_2,a_2,t_2,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(id_2,a_2,e,t_2,attrs_2)
+\\
+\quad\Rightarrow
+\exists id.~wasInformedBy(id,a_2,a_1,[])
+\end{array}</script></div>
+<div class="inference" number="7" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a href="#entity-generation-invalidation-inference" class="internalDFN">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-451-Frame" class="MathJax"><nobr><span id="MathJax-Span-8368" class="math"><span style="display: inline-block; position: relative; width: 693px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.032em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8369" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8370" class="mtable"><span style="display: inline-block; position: relative; width: 40.129em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.485em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 40.129em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8371" class="mtd"><span id="MathJax-Span-8372" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8373" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8374" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8376" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8377" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8378" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8379" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8380" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8381" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8382" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.303em; left: 0em;"><span id="MathJax-Span-8383" class="mtd"><span id="MathJax-Span-8384" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8385" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8387" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8388" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8389" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8391" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8392" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8393" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8394" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8395" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8397" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8398" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8399" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8400" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.036em; left: 0em;"><span id="MathJax-Span-8401" class="mtd"><span id="MathJax-Span-8402" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8403" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8404" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8405" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8406" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8407" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8408" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8409" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8410" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8411" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8412" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8413" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8414" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8415" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8416" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8417" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8418" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8419" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8420" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8421" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8422" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8423" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8424" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8425" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8426" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8428" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8429" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8430" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8431" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8432" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8433" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8434" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8435" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8436" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8437" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8438" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8439" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8441" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8442" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8443" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8444" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8445" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8446" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8447" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8448" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8450" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8451" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8453" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8454" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8455" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8456" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8457" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8458" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8459" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8460" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8461" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8462" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8463" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8464" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8466" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8467" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8468" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8469" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8471" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8472" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8473" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8476" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8477" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8478" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8479" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8480" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8481" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8482" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8483" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8484" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8485" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8486" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8487" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8488" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8489" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8490" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8491" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8492" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8493" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8494" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8495" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8496" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8497" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.99em; vertical-align: -3.071em;"></span></span></nobr></span><script id="MathJax-Element-451" type="math/tex">\begin{array}[t]{l}
+\forall e,attrs.~
+\\
+\qquad entity(e,attrs)
+\\
+\quad\Rightarrow
+\exists gen,a_1,t_1,inv,a_2,t_2.~wasGeneratedBy(gen,e,a_1,t_1,[]) \wedge wasInvalidatedBy(inv,e,a_2,t_2,[])
+\end{array}</script></div>
+<div class="inference" number="8" id="activity-start-end-inference"><div class="ruleTitle"><a href="#activity-start-end-inference" class="internalDFN">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-452-Frame" class="MathJax"><nobr><span id="MathJax-Span-8498" class="math"><span style="display: inline-block; position: relative; width: 716px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.041em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8499" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8500" class="mtable"><span style="display: inline-block; position: relative; width: 41.472em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.494em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 41.472em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8501" class="mtd"><span id="MathJax-Span-8502" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8503" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8504" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8505" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8506" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8507" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8508" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8509" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8510" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8511" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8512" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8513" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8514" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8515" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8516" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8517" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8518" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8519" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8520" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.294em; left: 0em;"><span id="MathJax-Span-8521" class="mtd"><span id="MathJax-Span-8522" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8523" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8524" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8525" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8527" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8528" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8529" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8531" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8532" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8533" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8534" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8535" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8537" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8538" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8539" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8541" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8542" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8545" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8546" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8547" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8548" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.045em; left: 0em;"><span id="MathJax-Span-8549" class="mtd"><span id="MathJax-Span-8550" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8551" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8552" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8553" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8554" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8557" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8559" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8560" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8561" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8562" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8563" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8564" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8565" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8566" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8567" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8569" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8570" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8574" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8577" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8578" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8579" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8580" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8581" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8583" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8584" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8585" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8586" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8587" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8588" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8590" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8591" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8592" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8593" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8594" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8596" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8597" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8598" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8599" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8600" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8601" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8603" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8604" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8605" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8606" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8607" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8608" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8609" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8613" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8614" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8615" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8616" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8617" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8618" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8619" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8620" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8621" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8622" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8623" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8624" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8625" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8626" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8627" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8628" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8630" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8631" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8632" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8633" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8634" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8635" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8636" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8637" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8638" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8639" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8640" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8641" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8642" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8643" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8645" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8646" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8647" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8648" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8649" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.999em; vertical-align: -3.081em;"></span></span></nobr></span><script id="MathJax-Element-452" type="math/tex">\begin{array}[t]{l}
+\forall a,t_1,t_2,attrs.~
+\\
+\qquad activity(a,t_1,t_2,attrs)
+\\
+\quad\Rightarrow
+\exists start,e_1,a_1,end,a_2,e_2.~wasStartedBy(start,a,e_1,a_1,t_1,[]) \wedge wasEndedBy(end,a,e_2,a_2,t_2,[])
+\end{array}</script></div>
+<div class="inference" number="9" id="wasStartedBy-inference"><div class="ruleTitle"><a href="#wasStartedBy-inference" class="internalDFN">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-453-Frame" class="MathJax"><nobr><span id="MathJax-Span-8650" class="math"><span style="display: inline-block; position: relative; width: 352px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.048em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8651" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8652" class="mtable"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8653" class="mtd"><span id="MathJax-Span-8654" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8655" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8656" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8657" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8658" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8659" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8660" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8661" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8662" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8663" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8664" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8665" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8666" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8667" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8668" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8669" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8670" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8672" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8674" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8675" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8676" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8677" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8678" class="mtd"><span id="MathJax-Span-8679" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8680" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8681" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8682" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8683" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8684" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8685" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8686" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8687" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8688" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8689" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8690" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8691" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8692" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8693" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8694" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8695" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8696" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8697" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8698" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8699" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8700" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8701" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8702" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8703" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8704" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8705" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8706" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8707" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8708" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8709" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8711" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8712" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8713" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8714" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-8715" class="mtd"><span id="MathJax-Span-8716" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8717" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8718" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8719" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8720" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8721" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8722" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8723" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8724" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8725" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8726" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8727" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8728" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8729" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8730" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8731" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8732" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8733" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8734" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8735" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8736" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8737" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8740" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8741" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8742" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8743" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8744" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8745" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8746" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8747" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8748" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8749" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8750" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8751" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8752" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8753" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8754" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8755" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8757" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8758" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8759" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8760" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8761" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8762" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.007em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-453" type="math/tex">\begin{array}[t]{l}
+\forall id,a,e_1,a_1,t,attrs.~
+\\
+\qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
+\\
+\quad\Rightarrow
+\exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
+\end{array}</script></div>
+<div class="inference" number="10" id="wasEndedBy-inference"><div class="ruleTitle"><a href="#wasEndedBy-inference" class="internalDFN">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-454-Frame" class="MathJax"><nobr><span id="MathJax-Span-8763" class="math"><span style="display: inline-block; position: relative; width: 352px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.048em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8764" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8765" class="mtable"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 20.21em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8766" class="mtd"><span id="MathJax-Span-8767" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8768" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8769" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8770" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8771" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8772" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8773" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8774" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8775" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8776" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8777" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8778" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8779" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8780" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8781" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8783" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8784" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8785" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8786" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8787" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8788" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8789" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8790" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-8791" class="mtd"><span id="MathJax-Span-8792" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8793" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8794" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8795" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8796" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8797" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8798" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8799" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8800" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8801" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8802" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8803" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8804" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8805" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8806" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8807" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8808" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8809" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8810" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8811" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8812" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8813" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8814" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8815" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8816" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8817" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8818" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8819" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8820" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8821" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8822" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8823" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8824" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8825" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-8826" class="mtd"><span id="MathJax-Span-8827" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-8828" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8829" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-8830" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8831" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8832" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8833" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8834" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8835" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8837" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8838" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8839" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8840" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8841" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8842" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8843" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8844" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8845" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8846" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8847" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8848" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8849" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8851" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8852" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8853" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8854" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8855" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8856" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8857" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8858" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8859" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8860" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8861" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8862" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8863" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8864" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8865" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8866" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8867" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8869" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8870" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8871" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8872" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8873" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.007em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-454" type="math/tex">\begin{array}[t]{l}
+\forall id,a,e_1,a_1,t,attrs.~
+\\
+\qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
+\\
+\quad\Rightarrow
+\exists gen,t_1.~wasGeneratedBy(gen,e_1,a_1,t_1,[])
+\end{array}</script></div>
+<div class="inference" number="11" id="derivation-generation-use-inference"><div class="ruleTitle"><a href="#derivation-generation-use-inference" class="internalDFN">Inference 11 (derivation-generation-use-inference)</a></div><p>In this inference, none of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-455-Frame" class="MathJax"><nobr><span id="MathJax-Span-8874" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8875" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8876" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-455" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-456-Frame" class="MathJax"><nobr><span id="MathJax-Span-8877" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8878" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8879" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8880" class="mi">e</span><span id="MathJax-Span-8881" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8882" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8883" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-456" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-457-Frame" class="MathJax"><nobr><span id="MathJax-Span-8884" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8885" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8886" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8887" class="mi">s</span><span id="MathJax-Span-8888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8889" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8890" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-457" type="math/tex">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-458-Frame" class="MathJax"><nobr><span id="MathJax-Span-8891" class="math"><span style="display: inline-block; position: relative; width: 690px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-8892" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-8893" class="mtable"><span style="display: inline-block; position: relative; width: 39.953em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 39.953em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-8894" class="mtd"><span id="MathJax-Span-8895" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-8896" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8897" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8898" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8899" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8900" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8901" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8902" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8903" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-8904" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8905" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8906" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8907" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8908" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8909" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8910" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8911" class="mi">e</span><span id="MathJax-Span-8912" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8913" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8914" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8915" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8916" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8917" class="mi">s</span><span id="MathJax-Span-8918" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8919" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8920" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8921" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8922" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8923" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8924" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8925" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8926" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8927" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-8928" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-8929" class="mtd"><span id="MathJax-Span-8930" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-8931" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8932" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8933" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8934" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8935" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8936" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8937" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8938" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8939" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8940" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-8941" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-8942" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-8943" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8944" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8945" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-8946" class="mi">N<span style="display: inline-block; overflow: hidden; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-8997" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-8998" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-8999" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9000" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9001" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9002" class="mi">e</span><span id="MathJax-Span-9003" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9004" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9005" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9007" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9008" class="mi">s</span><span id="MathJax-Span-9009" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9010" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9011" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9012" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9013" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9015" class="mi">t<span style="display: inline-block; overflow: hidden; 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position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9025" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9026" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); 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font-style: italic;" id="MathJax-Span-9064" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9065" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9066" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9067" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9068" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9069" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9070" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9071" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9072" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9073" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9074" class="mi">e</span><span id="MathJax-Span-9075" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9076" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9077" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9078" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9080" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9081" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9083" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9086" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9088" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9089" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9090" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9091" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-458" type="math/tex">\begin{array}[t]{l}
+\forall id,e_2,e_1,a,gen_2,use_1,attrs.~
+\\
+\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(id,e_2,e_1,a,gen_2,use_1,attrs)
+\\
+\quad\Rightarrow
+\exists t_1,t_2.~used(use_1,a,e_1,t_1,[]) \wedge wasGeneratedBy(gen_2,e_2,a,t_2,[])
+\end{array}</script></div>
+<div class="inference" number="12" id="revision-is-alternate-inference"><div class="ruleTitle"><a href="#revision-is-alternate-inference" class="internalDFN">Inference 12 (revision-is-alternate-inference)</a></div><p>In this inference, any of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-459-Frame" class="MathJax"><nobr><span id="MathJax-Span-9092" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9093" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9094" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-459" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-460-Frame" class="MathJax"><nobr><span id="MathJax-Span-9095" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9096" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9097" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9098" class="mi">e</span><span id="MathJax-Span-9099" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9100" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9101" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-460" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-461-Frame" class="MathJax"><nobr><span id="MathJax-Span-9102" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9103" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9104" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9105" class="mi">s</span><span id="MathJax-Span-9106" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9107" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9108" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-461" type="math/tex">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-462-Frame" class="MathJax"><nobr><span id="MathJax-Span-9109" class="math"><span style="display: inline-block; position: relative; width: 517px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9110" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9111" class="mtable"><span style="display: inline-block; position: relative; width: 29.848em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 29.848em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9112" class="mtd"><span id="MathJax-Span-9113" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9114" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9115" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9116" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9117" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9118" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9119" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9120" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9121" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9122" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9123" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9124" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9126" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9127" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9128" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9129" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9130" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9131" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9132" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-9133" class="mtd"><span id="MathJax-Span-9134" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9135" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9136" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9137" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9138" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9139" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9140" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9141" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9142" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9143" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9145" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9146" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9147" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9148" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9149" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9150" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9151" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9152" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9153" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9154" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9155" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9156" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9157" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9158" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9159" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9160" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9161" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9162" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9163" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9164" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9165" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9166" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9167" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9168" class="mo">[</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9169" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9170" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9171" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9172" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9173" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9175" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9176" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9177" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9178" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9179" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9180" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9181" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9182" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9183" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9184" class="mi">R</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9185" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9186" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9187" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9188" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9189" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9190" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9191" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9192" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9193" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9194" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-9195" class="mtd"><span id="MathJax-Span-9196" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9197" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9198" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9199" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9200" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9201" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9203" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9204" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9207" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9208" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9209" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9210" class="mo">(</span><span id="MathJax-Span-9211" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9212" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9213" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9214" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9215" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9216" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9217" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9218" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-462" type="math/tex">\begin{array}[t]{l}
+\forall id,e_1,e_2,a,g,u.~
+\\
+\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,[prov:type = prov:Revision]))
+\\
+\quad\Rightarrow
+alternateOf(e_2,e_1)
+\end{array}</script></div>
+<div class="inference" number="13" id="attribution-inference"><div class="ruleTitle"><a href="#attribution-inference" class="internalDFN">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-463-Frame" class="MathJax"><nobr><span id="MathJax-Span-9219" class="math"><span style="display: inline-block; position: relative; width: 691px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9220" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9221" class="mtable"><span style="display: inline-block; position: relative; width: 40.012em; height: 0px;"><span style="position: absolute; clip: rect(3.719em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 40.012em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9222" class="mtd"><span id="MathJax-Span-9223" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9224" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9226" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9228" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9229" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9230" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9231" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9232" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9233" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9234" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9235" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9236" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9237" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9238" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9239" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9240" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-9241" class="mtd"><span id="MathJax-Span-9242" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9243" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9244" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9245" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9246" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9247" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9250" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9251" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9252" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9253" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9255" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9256" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9257" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9258" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9259" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9262" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9263" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9264" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9265" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9266" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9267" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9268" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9269" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9272" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9273" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9274" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-9275" class="mtd"><span id="MathJax-Span-9276" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9277" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9278" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9279" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9280" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9281" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9282" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9283" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9284" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9285" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9286" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9287" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9288" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9290" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9291" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9292" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9294" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9295" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9296" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9297" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9298" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9299" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9300" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9301" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9302" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9303" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9304" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9305" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9306" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9307" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9308" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9309" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9310" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9311" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9312" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9313" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9314" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9315" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9316" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9317" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9318" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9319" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9320" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9321" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9322" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9323" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9324" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9325" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-9326" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-9327" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9328" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9329" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9330" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9331" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9332" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9333" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9334" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9335" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9336" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9338" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9339" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9340" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9341" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9342" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9343" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9346" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9347" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9348" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9349" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9350" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9351" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9353" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9354" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9355" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9356" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9357" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9358" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9359" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9360" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9361" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-463" type="math/tex">\begin{array}[t]{l}
+\forall att,e,ag,attrs.~
+\\
+\qquad wasAttributedTo(att,e,ag,attrs)
+\\
+\quad\Rightarrow
+\exists a,t,gen,assoc,pl.~wasGeneratedBy(gen,e,a,t,[]) \wedge wasAssociatedWith(assoc,a,ag,pl,[])
+\end{array}</script></div>
+<div class="inference" number="14" id="delegation-inference"><div class="ruleTitle"><a href="#delegation-inference" class="internalDFN">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-464-Frame" class="MathJax"><nobr><span id="MathJax-Span-9362" class="math"><span style="display: inline-block; position: relative; width: 722px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.21em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9363" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9364" class="mtable"><span style="display: inline-block; position: relative; width: 41.822em; height: 0px;"><span style="position: absolute; clip: rect(3.815em, 1000em, 7.838em, -0.526em); top: -4.673em; left: 0em;"><span style="display: inline-block; position: relative; width: 41.822em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9365" class="mtd"><span id="MathJax-Span-9366" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9367" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9368" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9369" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9370" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9371" class="mi">a</span><span id="MathJax-Span-9372" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9373" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9374" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9376" class="mi">a</span><span id="MathJax-Span-9377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9378" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9380" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9381" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9382" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9384" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9385" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9386" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9387" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9388" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9389" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-9390" class="mtd"><span id="MathJax-Span-9391" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9392" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9394" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9395" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9396" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9397" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9398" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9399" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9400" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9401" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9402" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9403" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9404" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9405" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9406" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9407" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9408" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9409" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9410" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9411" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9412" class="mi">a</span><span id="MathJax-Span-9413" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9414" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9415" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9416" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9417" class="mi">a</span><span id="MathJax-Span-9418" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9419" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9420" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9421" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9422" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9423" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9425" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9427" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9428" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9429" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-9430" class="mtd"><span id="MathJax-Span-9431" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9432" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9433" class="mo">⇒</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-9434" class="mi">∃</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9435" class="mi">i</span><span id="MathJax-Span-9436" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9437" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9438" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9439" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9440" class="mi">p</span><span id="MathJax-Span-9441" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9442" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9443" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9444" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9445" class="mi">i</span><span id="MathJax-Span-9446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9447" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9448" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9450" class="mi">p</span><span id="MathJax-Span-9451" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9452" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9453" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9454" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9455" class="mtext"> </span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9456" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9457" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9458" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9459" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9460" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9461" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9462" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9463" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9465" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9466" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9468" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9469" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9470" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9472" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9473" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9474" class="mi">i</span><span id="MathJax-Span-9475" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9476" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9477" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9478" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9479" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9481" class="mi">a</span><span id="MathJax-Span-9482" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9483" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9484" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9485" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9486" class="mi">p</span><span id="MathJax-Span-9487" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9488" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9489" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9490" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9491" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9492" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9493" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-9494" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-9495" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9496" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9497" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9498" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9499" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9500" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9501" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9502" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9504" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9505" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9506" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9507" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9508" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9509" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9511" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9513" class="mi">i</span><span id="MathJax-Span-9514" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9515" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9516" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9517" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9518" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9519" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9520" class="mi">a</span><span id="MathJax-Span-9521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9522" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9523" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9524" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9525" class="mi">p</span><span id="MathJax-Span-9526" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.485em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9527" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9528" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9529" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9530" class="mo">[</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9531" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9532" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.18em; vertical-align: -3.262em;"></span></span></nobr></span><script id="MathJax-Element-464" type="math/tex">\begin{array}[t]{l}
+\forall id,ag_1,ag_2,a,attrs.~
+\\
+\qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
+\\
+\quad\Rightarrow
+\exists id_1,pl_1,id_2,pl_2.~wasAssociatedWith(id_1,a,ag_1,pl_1,[]) \wedge wasAssociatedWith(id_2,a,ag_2,pl_2,[])
+\end{array}</script></div>
+<div class="inference" number="15" id="influence-inference"><div class="ruleTitle"><a href="#influence-inference" class="internalDFN">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-465-Frame" class="MathJax"><nobr><span id="MathJax-Span-9533" class="math"><span style="display: inline-block; position: relative; width: 271px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.04em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9534" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9535" class="mtable"><span style="display: inline-block; position: relative; width: 15.479em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.493em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.479em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9536" class="mtd"><span id="MathJax-Span-9537" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9538" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9539" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9540" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9541" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9542" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9543" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9544" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9545" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9547" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9548" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9550" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9551" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9552" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9553" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9554" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-9555" class="mtd"><span id="MathJax-Span-9556" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9557" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9558" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9560" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9561" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9562" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9563" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9564" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9565" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9566" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9567" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9568" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9569" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9570" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9571" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9572" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9573" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9574" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9575" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9576" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9577" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9578" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9579" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9581" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9584" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9585" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9586" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9587" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.043em; left: 0em;"><span id="MathJax-Span-9588" class="mtd"><span id="MathJax-Span-9589" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9590" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9591" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9592" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9593" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9594" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9595" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9596" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9597" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9598" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9599" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9602" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9603" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9604" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9605" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9606" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9607" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9608" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9609" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9610" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9611" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9612" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9613" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9614" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9615" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9616" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9618" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9619" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9620" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.998em; vertical-align: -3.08em;"></span></span></nobr></span><script id="MathJax-Element-465" type="math/tex">\begin{array}[t]{l}
+\forall id,e,a,t,attrs.~
+\\
+\qquad wasGeneratedBy(id,e,a,t,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,e,a,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-466-Frame" class="MathJax"><nobr><span id="MathJax-Span-9621" class="math"><span style="display: inline-block; position: relative; width: 263px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.011em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9622" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9623" class="mtable"><span style="display: inline-block; position: relative; width: 15.012em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.464em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.012em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9624" class="mtd"><span id="MathJax-Span-9625" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9626" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9627" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9628" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9629" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9630" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9631" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9632" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9633" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9634" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9635" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9636" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9637" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9638" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9639" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9640" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9641" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9642" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-9643" class="mtd"><span id="MathJax-Span-9644" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9645" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9646" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9647" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9648" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9649" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9650" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9651" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9652" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9653" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9654" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9656" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9657" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9659" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9663" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9664" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9665" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.014em; left: 0em;"><span id="MathJax-Span-9666" class="mtd"><span id="MathJax-Span-9667" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9668" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9669" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9670" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9672" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9673" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9674" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9675" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9676" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9677" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9678" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9679" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9680" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9681" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9682" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9683" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9684" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9685" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9686" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9687" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9688" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9689" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9690" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9691" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9692" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9693" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9694" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9695" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9696" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9697" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9698" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.967em; vertical-align: -3.049em;"></span></span></nobr></span><script id="MathJax-Element-466" type="math/tex">\begin{array}[t]{l}
+\forall id,a,e,t,attrs.~
+\\
+\qquad used(id,a,e,t,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,a,e,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-467-Frame" class="MathJax"><nobr><span id="MathJax-Span-9699" class="math"><span style="display: inline-block; position: relative; width: 280px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9700" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9701" class="mtable"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9702" class="mtd"><span id="MathJax-Span-9703" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9704" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9705" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9706" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9707" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9708" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9709" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9710" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9711" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9712" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9713" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9714" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9715" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9716" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9719" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9720" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9721" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9722" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9723" class="mtd"><span id="MathJax-Span-9724" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9725" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9726" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9727" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9728" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9729" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9730" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9731" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9732" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9733" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9734" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9735" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9736" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9737" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9738" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9739" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9740" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9741" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9742" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9743" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9744" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9745" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9746" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9747" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9748" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9749" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9750" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9751" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9753" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9754" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9755" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9756" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-9757" class="mtd"><span id="MathJax-Span-9758" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9759" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9760" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9761" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9762" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9763" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9764" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9765" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9766" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9767" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9768" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9769" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9770" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9771" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9772" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9773" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9774" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9775" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9776" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9777" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9778" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9779" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9780" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9781" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9782" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9783" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9785" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9786" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9787" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9788" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9789" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9790" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9791" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9792" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9793" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-467" type="math/tex">\begin{array}[t]{l}
+\forall id,a_2,a_1,attrs.~
+\\
+\qquad wasInformedBy(id,a_2,a_1,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,a_2,a_1,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-468-Frame" class="MathJax"><nobr><span id="MathJax-Span-9794" class="math"><span style="display: inline-block; position: relative; width: 280px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.049em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9795" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9796" class="mtable"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.502em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 16.005em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9797" class="mtd"><span id="MathJax-Span-9798" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9799" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9800" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9801" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9802" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9804" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9805" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9806" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9807" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9808" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9809" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9810" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9811" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9812" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9813" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9814" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9815" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9819" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9820" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9821" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9822" class="mtd"><span id="MathJax-Span-9823" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9824" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9825" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9826" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9827" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9828" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9829" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9830" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9831" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9832" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9833" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9834" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9835" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9836" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9837" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9838" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9839" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9840" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9841" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9842" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9843" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9844" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9845" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9846" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9847" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9848" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9849" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9852" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9853" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9854" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9856" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9857" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9858" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-9859" class="mtd"><span id="MathJax-Span-9860" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9861" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9862" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9863" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9864" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9865" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9866" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9867" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9868" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9869" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9870" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9871" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9872" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9873" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9874" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9875" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9876" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9877" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9878" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9879" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9880" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9881" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9882" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9883" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9884" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9886" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9887" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9888" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9890" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9891" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9892" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9893" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-468" type="math/tex">\begin{array}[t]{l}
+\forall id,a_2,e,a_1,t,attrs.~
+\\
+\qquad wasStartedBy(id,a_2,e,a_1,t,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,a_2,e,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-469-Frame" class="MathJax"><nobr><span id="MathJax-Span-9894" class="math"><span style="display: inline-block; position: relative; width: 274px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.049em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9895" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9896" class="mtable"><span style="display: inline-block; position: relative; width: 15.654em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.502em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.654em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9897" class="mtd"><span id="MathJax-Span-9898" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9899" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9900" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9901" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9902" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9903" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9904" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9905" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9906" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9907" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9908" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9909" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9910" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9911" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9912" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9914" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9917" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9918" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9919" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9920" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-9921" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-9922" class="mtd"><span id="MathJax-Span-9923" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-9924" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9925" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9926" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9927" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9928" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9929" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9930" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9931" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9932" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9933" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9934" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9935" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9936" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9937" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9938" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9939" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9940" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9941" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9942" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9943" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9944" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9946" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9948" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9949" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9950" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9951" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9954" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9955" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9956" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-9957" class="mtd"><span id="MathJax-Span-9958" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-9959" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9960" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-9961" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9962" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9963" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9965" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9966" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9967" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9968" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9969" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9970" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9971" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9978" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9979" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-9980" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9981" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9982" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-9983" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9984" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9985" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-9986" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9987" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9989" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9990" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-9991" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.008em; vertical-align: -3.09em;"></span></span></nobr></span><script id="MathJax-Element-469" type="math/tex">\begin{array}[t]{l}
+\forall id,a_2,e,a_1,t,attrs.~
+\\
+\qquad wasEndedBy(id,a_2,e,a_1,t,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,a_2,e,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-470-Frame" class="MathJax"><nobr><span id="MathJax-Span-9992" class="math"><span style="display: inline-block; position: relative; width: 278px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.04em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-9993" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-9994" class="mtable"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.493em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-9995" class="mtd"><span id="MathJax-Span-9996" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-9997" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9998" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-9999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10000" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10001" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10002" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10003" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10004" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10007" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10010" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10011" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10012" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10013" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-10014" class="mtd"><span id="MathJax-Span-10015" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10016" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10017" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10018" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10019" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10020" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10021" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10022" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10023" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10024" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10025" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10026" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10027" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10029" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10030" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10031" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10032" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10033" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10034" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10035" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10036" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10037" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10038" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10039" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10040" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10041" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10043" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-10062" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10063" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10064" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10065" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10066" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10067" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10068" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10069" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10070" class="mi">d<span style="display: inline-block; overflow: hidden; 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font-style: italic;" id="MathJax-Span-10125" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10126" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10127" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10128" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10129" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10130" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10131" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10132" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10133" class="msubsup"><span style="display: inline-block; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10139" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10140" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10141" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10142" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10143" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10144" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10145" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10146" class="mo">,</span><span style="font-family: STIXGeneral; 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height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10170" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10171" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10172" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10173" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10174" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10175" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10177" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10178" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10179" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10180" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10181" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10182" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10183" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10184" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10185" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10186" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10187" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10188" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10189" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-471" type="math/tex">\begin{array}[t]{l}
+\forall id,e_2,e_1,a,g,u,attrs.~
+\\
+\qquad wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,e_2,e_1,attrs)
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-472-Frame" class="MathJax"><nobr><span id="MathJax-Span-10190" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10191" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10192" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-472" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-473-Frame" class="MathJax"><nobr><span id="MathJax-Span-10193" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10194" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10195" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-473" type="math/tex">g</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-474-Frame" class="MathJax"><nobr><span id="MathJax-Span-10196" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10197" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10198" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-474" type="math/tex">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-475-Frame" class="MathJax"><nobr><span id="MathJax-Span-10199" class="math"><span style="display: inline-block; position: relative; width: 272px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10200" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10201" class="mtable"><span style="display: inline-block; position: relative; width: 15.537em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.537em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10202" class="mtd"><span id="MathJax-Span-10203" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10204" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10205" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10206" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10207" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10208" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10209" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10210" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10211" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10212" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10213" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10215" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10216" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10217" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10218" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10219" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-10220" class="mtd"><span id="MathJax-Span-10221" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10222" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10223" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10224" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10225" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10226" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10229" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10230" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10231" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10232" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10234" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10235" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10236" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10237" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10238" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10239" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10240" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10241" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10242" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10243" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10244" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10245" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10247" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10249" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10250" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10251" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10252" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-10253" class="mtd"><span id="MathJax-Span-10254" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10255" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10256" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10257" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10258" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10259" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10260" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10261" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10262" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10263" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10264" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10265" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10266" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10267" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10268" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10269" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10270" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10271" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10272" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10273" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10274" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10276" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10279" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10280" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10281" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10282" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10284" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10285" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10286" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-475" type="math/tex">\begin{array}[t]{l}
+\forall id,e,ag,attrs.~
+\\
+\qquad wasAttributedTo(id,e,ag,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,e,ag,attrs)
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-476-Frame" class="MathJax"><nobr><span id="MathJax-Span-10287" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10288" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10289" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10290" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-476" type="math/tex">pl</script> may be a placeholder -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-477-Frame" class="MathJax"><nobr><span id="MathJax-Span-10291" class="math"><span style="display: inline-block; position: relative; width: 307px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10292" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10293" class="mtable"><span style="display: inline-block; position: relative; width: 17.582em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.582em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10294" class="mtd"><span id="MathJax-Span-10295" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10296" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10297" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10298" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10300" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10301" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10302" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10303" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10305" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10306" class="mi">l<span style="display: inline-block; 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font-style: italic;" id="MathJax-Span-10371" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10372" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10373" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10374" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10375" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10376" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10377" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10378" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10379" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10380" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10381" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10382" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10384" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10385" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10386" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-477" type="math/tex">\begin{array}[t]{l}
+\forall id,a,ag,pl,attrs.~
+\\
+\qquad wasAssociatedWith(id,a,ag,pl,attrs)
+\\
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+wasInfluencedBy(id,a,ag,attrs)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-478-Frame" class="MathJax"><nobr><span id="MathJax-Span-10387" class="math"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.21em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10388" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10389" class="mtable"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(3.815em, 1000em, 7.838em, -0.526em); top: -4.673em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10390" class="mtd"><span id="MathJax-Span-10391" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10392" class="mi">∀</span><span style="font-family: STIXGeneral; 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padding-left: 0.188em;" id="MathJax-Span-10414" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-10415" class="mtd"><span id="MathJax-Span-10416" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10417" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10418" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10419" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10420" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10421" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10422" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10423" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10424" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10425" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10426" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10427" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10428" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10429" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10430" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10431" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10432" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10433" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10434" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10435" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10436" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10437" class="mi">a</span><span id="MathJax-Span-10438" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10439" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10440" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10441" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10442" class="mi">a</span><span id="MathJax-Span-10443" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10444" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10445" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10446" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10447" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10448" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10449" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10450" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10452" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10453" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10454" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-10455" class="mtd"><span id="MathJax-Span-10456" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10457" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10458" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10459" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10460" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10461" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10462" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10463" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10464" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10465" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10466" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10467" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10468" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10469" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10470" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10471" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10472" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10473" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10474" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10475" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10476" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10477" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10478" class="mi">a</span><span id="MathJax-Span-10479" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10480" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10481" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10482" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10483" class="mi">a</span><span id="MathJax-Span-10484" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10485" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10486" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10487" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10490" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10491" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10492" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10493" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.18em; vertical-align: -3.262em;"></span></span></nobr></span><script id="MathJax-Element-478" type="math/tex">\begin{array}[t]{l}
+\forall id,ag_2,ag_1,a,attrs.~
+\\
+\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
+\\
+\quad\Rightarrow
+wasInfluencedBy(id,ag_2,ag_1,attrs)
+\end{array}</script></li></ol></div>
+<div class="inference" number="16" id="alternate-reflexive"><div class="ruleTitle"><a href="#alternate-reflexive" class="internalDFN">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-479-Frame" class="MathJax"><nobr><span id="MathJax-Span-10494" class="math"><span style="display: inline-block; position: relative; width: 163px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.966em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10495" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10496" class="mtable"><span style="display: inline-block; position: relative; width: 9.171em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.302em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.171em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.756em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10497" class="mtd"><span id="MathJax-Span-10498" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10499" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10500" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10501" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10502" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-10503" class="mtd"><span id="MathJax-Span-10504" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10505" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10506" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10507" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10508" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10509" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10511" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10513" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10514" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -0.031em; left: 0em;"><span id="MathJax-Span-10515" class="mtd"><span id="MathJax-Span-10516" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10517" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10518" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10519" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10520" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10521" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10522" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10523" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10524" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10525" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10527" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10528" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10529" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10530" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10531" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10533" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10534" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.919em; vertical-align: -3.001em;"></span></span></nobr></span><script id="MathJax-Element-479" type="math/tex">\begin{array}[t]{l}
+\forall e.~
+\\
+\qquad entity(e)
+\\
+\quad\Rightarrow
+alternateOf(e,e)
+\end{array}</script></div>
+<div class="proof">
+ <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-480-Frame" class="MathJax"><nobr><span id="MathJax-Span-10535" class="math"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10536" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10537" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10538" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10540" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10541" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10542" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10543" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10544" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10545" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10546" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-480" type="math/tex">ent = rho(e)</script>. Clearly <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-481-Frame" class="MathJax"><nobr><span id="MathJax-Span-10547" class="math"><span style="display: inline-block; position: relative; width: 83px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.772em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10548" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10549" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10550" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10551" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10552" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10554" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10556" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10557" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10558" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.854em; vertical-align: -0.091em;"></span></span></nobr></span><script id="MathJax-Element-481" type="math/tex">e \in Entities</script> and
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-482-Frame" class="MathJax"><nobr><span id="MathJax-Span-10559" class="math"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10560" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10561" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10562" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10563" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10564" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10565" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10566" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10567" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10568" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10569" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10570" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10571" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10573" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10574" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10575" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10576" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10577" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10578" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10579" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10580" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10581" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-482" type="math/tex">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-483-Frame" class="MathJax"><nobr><span id="MathJax-Span-10582" class="math"><span style="display: inline-block; position: relative; width: 171px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10583" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10584" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10585" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10586" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10587" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10588" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10589" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10590" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10592" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10593" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10596" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10597" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10598" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10599" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10600" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10601" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10602" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10603" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-483" type="math/tex">W,\rho \models alternateOf(e,e)</script>.</p>
+ </div>
+<div class="inference" number="17" id="alternate-transitive"><div class="ruleTitle"><a href="#alternate-transitive" class="internalDFN">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-484-Frame" class="MathJax"><nobr><span id="MathJax-Span-10604" class="math"><span style="display: inline-block; position: relative; width: 328px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.06em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10605" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10606" class="mtable"><span style="display: inline-block; position: relative; width: 18.808em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.513em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.808em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10607" class="mtd"><span id="MathJax-Span-10608" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10609" class="mi">∀</span><span id="MathJax-Span-10610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10611" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10613" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10614" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10615" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10616" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10617" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10618" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10619" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10620" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10621" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10622" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-10623" class="mtd"><span id="MathJax-Span-10624" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10625" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10626" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10627" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10628" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10631" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10632" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10633" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10634" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10635" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10636" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10637" class="mo">(</span><span id="MathJax-Span-10638" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10639" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10640" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10641" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10642" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10643" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10644" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10645" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-10646" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-10647" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10651" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10652" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10653" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10655" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10656" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10657" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10658" class="mo">(</span><span id="MathJax-Span-10659" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10660" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10661" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10662" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10663" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10664" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10665" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10666" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.063em; left: 0em;"><span id="MathJax-Span-10667" class="mtd"><span id="MathJax-Span-10668" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10669" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10670" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10671" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10672" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10673" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10674" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10675" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10676" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10677" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10678" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10679" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10680" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10681" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10682" class="mo">(</span><span id="MathJax-Span-10683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10684" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10686" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10687" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10688" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10689" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10690" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.02em; vertical-align: -3.101em;"></span></span></nobr></span><script id="MathJax-Element-484" type="math/tex">\begin{array}[t]{l}
+\forall e_1,e_2,e_3.~
+\\
+\qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
+\\
+\quad\Rightarrow
+alternateOf(e_1,e_3)
+\end{array}</script></div>
+<div class="proof">
+ <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-485-Frame" class="MathJax"><nobr><span id="MathJax-Span-10691" class="math"><span style="display: inline-block; position: relative; width: 101px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10692" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10693" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10694" class="mi">n</span><span id="MathJax-Span-10695" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10697" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10698" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10699" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10700" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10701" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10702" class="mo">(</span><span id="MathJax-Span-10703" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10704" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10705" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10706" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-485" type="math/tex">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-486-Frame" class="MathJax"><nobr><span id="MathJax-Span-10707" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10708" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10709" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10710" class="mi">n</span><span id="MathJax-Span-10711" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10713" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10714" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10715" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10716" class="mo">(</span><span id="MathJax-Span-10717" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10718" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10719" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10720" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-486" type="math/tex">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-487-Frame" class="MathJax"><nobr><span id="MathJax-Span-10721" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10722" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10723" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10724" class="mi">n</span><span id="MathJax-Span-10725" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10726" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10727" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10728" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10729" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10730" class="mo">(</span><span id="MathJax-Span-10731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10733" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10734" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-487" type="math/tex">ent_3 = \rho(e_3)</script>. Then by
+ assumption <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-488-Frame" class="MathJax"><nobr><span id="MathJax-Span-10735" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10736" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10737" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10738" class="mi">n</span><span id="MathJax-Span-10739" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10740" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10741" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-488" type="math/tex">ent_1</script>, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-489-Frame" class="MathJax"><nobr><span id="MathJax-Span-10742" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10743" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10744" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10745" class="mi">n</span><span id="MathJax-Span-10746" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10747" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10748" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-489" type="math/tex">ent_2</script>, and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-490-Frame" class="MathJax"><nobr><span id="MathJax-Span-10749" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10750" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10751" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10752" class="mi">n</span><span id="MathJax-Span-10753" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10754" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10755" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.88em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-490" type="math/tex">ent_3</script> are in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-491-Frame" class="MathJax"><nobr><span id="MathJax-Span-10756" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.758em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10757" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10758" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10759" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10761" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10762" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10764" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10765" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.839em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-491" type="math/tex">Entities</script> and
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-492-Frame" class="MathJax"><nobr><span id="MathJax-Span-10766" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10767" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10769" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10771" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10772" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10773" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10774" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10775" class="mo">(</span><span id="MathJax-Span-10776" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10777" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10778" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10779" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10780" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10782" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10783" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10784" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10785" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10786" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10787" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10788" class="mo">(</span><span id="MathJax-Span-10789" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10790" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10791" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10792" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-492" type="math/tex">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-493-Frame" class="MathJax"><nobr><span id="MathJax-Span-10793" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10794" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10796" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10797" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10798" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10799" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10800" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10801" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10802" class="mo">(</span><span id="MathJax-Span-10803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10804" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10805" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10806" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10807" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10809" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10810" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10811" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10812" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10813" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10814" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10815" class="mo">(</span><span id="MathJax-Span-10816" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10817" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10818" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10819" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-493" type="math/tex">thingOf(e_2) = thingOf(e_3)</script>, so
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-494-Frame" class="MathJax"><nobr><span id="MathJax-Span-10820" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10821" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10822" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10823" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10824" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10825" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10826" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10827" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10828" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10829" class="mo">(</span><span id="MathJax-Span-10830" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10831" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10832" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10833" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10834" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10836" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10837" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10838" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10839" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10840" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10841" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10842" class="mo">(</span><span id="MathJax-Span-10843" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10844" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10845" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10846" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-494" type="math/tex">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-495-Frame" class="MathJax"><nobr><span id="MathJax-Span-10847" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10848" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10849" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-10851" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10852" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10853" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10854" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10855" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10856" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10857" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10858" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10861" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10862" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10863" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10864" class="mo">(</span><span id="MathJax-Span-10865" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10866" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10867" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10868" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10869" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10870" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10871" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10872" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-495" type="math/tex">W,\rho
+ \models alternateOf(e_2,e_1)</script>.</p>
+ </div>
+<div class="inference" number="18" id="alternate-symmetric"><div class="ruleTitle"><a href="#alternate-symmetric" class="internalDFN">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-496-Frame" class="MathJax"><nobr><span id="MathJax-Span-10873" class="math"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-10874" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-10875" class="mtable"><span style="display: inline-block; position: relative; width: 10.047em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.047em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10876" class="mtd"><span id="MathJax-Span-10877" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-10878" class="mi">∀</span><span id="MathJax-Span-10879" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10880" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10881" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10882" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10883" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10884" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10885" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10886" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-10887" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-10888" class="mtd"><span id="MathJax-Span-10889" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-10890" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10891" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10892" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10895" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10896" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10897" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10898" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10899" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10900" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10901" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10902" class="mo">(</span><span id="MathJax-Span-10903" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10904" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10905" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10906" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10907" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10908" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10909" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10910" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-10911" class="mtd"><span id="MathJax-Span-10912" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-10913" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10914" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10915" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10916" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10917" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10918" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10919" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10920" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10921" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10922" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10923" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10924" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10925" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10926" class="mo">(</span><span id="MathJax-Span-10927" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10928" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10929" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10930" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-10931" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10932" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10933" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10934" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-496" type="math/tex">\begin{array}[t]{l}
+\forall e_1,e_2.~
+\\
+\qquad alternateOf(e_1,e_2)
+\\
+\quad\Rightarrow
+alternateOf(e_2,e_1)
+\end{array}</script></div>
+<div class="proof">
+ <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-497-Frame" class="MathJax"><nobr><span id="MathJax-Span-10935" class="math"><span style="display: inline-block; position: relative; width: 101px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10936" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10937" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10938" class="mi">n</span><span id="MathJax-Span-10939" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10941" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10942" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10943" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10944" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10945" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10946" class="mo">(</span><span id="MathJax-Span-10947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10948" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10950" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-497" type="math/tex">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-498-Frame" class="MathJax"><nobr><span id="MathJax-Span-10951" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10952" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10953" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10954" class="mi">n</span><span id="MathJax-Span-10955" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10957" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-10958" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-10959" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-10960" class="mo">(</span><span id="MathJax-Span-10961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10962" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10963" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10964" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-498" type="math/tex">ent_2 = \rho(e_2)</script>. Then by
+ assumption both <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-499-Frame" class="MathJax"><nobr><span id="MathJax-Span-10965" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10966" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10967" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10968" class="mi">n</span><span id="MathJax-Span-10969" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10971" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-499" type="math/tex">ent_1</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-500-Frame" class="MathJax"><nobr><span id="MathJax-Span-10972" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10973" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10974" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10975" class="mi">n</span><span id="MathJax-Span-10976" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10977" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10978" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-500" type="math/tex">ent_2</script> are in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-501-Frame" class="MathJax"><nobr><span id="MathJax-Span-10979" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.741em, 1000em, 2.758em, -0.527em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10980" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10981" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10982" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10983" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10984" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10985" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10986" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10987" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10988" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.839em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-501" type="math/tex">Entities</script> and
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-502-Frame" class="MathJax"><nobr><span id="MathJax-Span-10989" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-10990" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10992" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10993" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10994" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10995" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10996" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-10997" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-10998" class="mo">(</span><span id="MathJax-Span-10999" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11000" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11001" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11002" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11003" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11004" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11005" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11006" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11007" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11008" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11009" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11010" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11011" class="mo">(</span><span id="MathJax-Span-11012" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11013" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11014" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11015" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-502" type="math/tex">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-503-Frame" class="MathJax"><nobr><span id="MathJax-Span-11016" class="math"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11017" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11018" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11019" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11020" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11021" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11022" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11023" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11024" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11025" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11026" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11027" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11028" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11029" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11030" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11031" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11032" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11033" class="mo">(</span><span id="MathJax-Span-11034" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11035" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11036" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11037" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11038" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11039" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11040" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11041" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-503" type="math/tex">W,\rho
+ \models alternateOf(e_2,e_1)</script>.</p>
+ </div>
+
+<div class="inference" number="19" id="specialization-transitive"><div class="ruleTitle"><a href="#specialization-transitive" class="internalDFN">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-504-Frame" class="MathJax"><nobr><span id="MathJax-Span-11042" class="math"><span style="display: inline-block; position: relative; width: 393px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.06em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11043" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11044" class="mtable"><span style="display: inline-block; position: relative; width: 22.605em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.513em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 22.605em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11045" class="mtd"><span id="MathJax-Span-11046" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11047" class="mi">∀</span><span id="MathJax-Span-11048" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11049" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11050" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11054" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11058" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11059" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11060" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-11061" class="mtd"><span id="MathJax-Span-11062" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11063" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11064" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11065" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11066" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11067" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11068" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11069" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11070" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11071" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11072" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11073" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11074" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11075" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11076" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11077" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11078" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11079" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11080" class="mo">(</span><span id="MathJax-Span-11081" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11082" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11083" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11086" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11088" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-11089" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-11090" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11091" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11092" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11093" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11094" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11095" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11096" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11097" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11098" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11099" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11100" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11102" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11103" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11104" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11105" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11106" class="mo">(</span><span id="MathJax-Span-11107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11109" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11110" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11111" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11112" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11113" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11114" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.063em; left: 0em;"><span id="MathJax-Span-11115" class="mtd"><span id="MathJax-Span-11116" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11117" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11118" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11119" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11120" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11121" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11122" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11123" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11124" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11125" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11126" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11127" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11128" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11130" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11131" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11132" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11133" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11134" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11135" class="mo">(</span><span id="MathJax-Span-11136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11137" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11139" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11140" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11141" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11142" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11143" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.02em; vertical-align: -3.101em;"></span></span></nobr></span><script id="MathJax-Element-504" type="math/tex">\begin{array}[t]{l}
+\forall e_1,e_2,e_3.~
+\\
+\qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
+\\
+\quad\Rightarrow
+specializationOf(e_1,e_3)
+\end{array}</script></div>
+<div class="proof">
+ <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-505-Frame" class="MathJax"><nobr><span id="MathJax-Span-11144" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11145" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11146" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11147" class="mi">n</span><span id="MathJax-Span-11148" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11150" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-505" type="math/tex">ent_1</script> and
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-506-Frame" class="MathJax"><nobr><span id="MathJax-Span-11151" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11152" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11153" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11154" class="mi">n</span><span id="MathJax-Span-11155" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11156" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11157" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-506" type="math/tex">ent_2</script> and for <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-507-Frame" class="MathJax"><nobr><span id="MathJax-Span-11158" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.895em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11159" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11160" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11161" class="mi">n</span><span id="MathJax-Span-11162" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11163" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11164" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-507" type="math/tex">ent_2</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-508-Frame" class="MathJax"><nobr><span id="MathJax-Span-11165" class="math"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11166" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11167" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11168" class="mi">n</span><span id="MathJax-Span-11169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11171" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.88em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-508" type="math/tex">ent_3</script>, where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-509-Frame" class="MathJax"><nobr><span id="MathJax-Span-11172" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11173" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11174" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11175" class="mi">n</span><span id="MathJax-Span-11176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11177" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11178" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11179" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11180" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11181" class="mo">(</span><span id="MathJax-Span-11182" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11183" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11184" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11185" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-509" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-510-Frame" class="MathJax"><nobr><span id="MathJax-Span-11186" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11187" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11188" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11189" class="mi">n</span><span id="MathJax-Span-11190" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11191" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11192" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11193" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11194" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11195" class="mo">(</span><span id="MathJax-Span-11196" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11197" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11198" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11199" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-510" type="math/tex">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-511-Frame" class="MathJax"><nobr><span id="MathJax-Span-11200" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11201" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11202" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11203" class="mi">n</span><span id="MathJax-Span-11204" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11205" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11206" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11207" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11208" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11209" class="mo">(</span><span id="MathJax-Span-11210" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11211" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11212" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11213" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-511" type="math/tex">ent_3 =
+ \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-512-Frame" class="MathJax"><nobr><span id="MathJax-Span-11214" class="math"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.485em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11215" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11216" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11217" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11218" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11219" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11220" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11221" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11222" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11223" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11224" class="mo">(</span><span id="MathJax-Span-11225" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11226" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11227" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11228" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11229" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11230" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11231" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11232" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11233" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11234" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11236" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11237" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11238" class="mo">(</span><span id="MathJax-Span-11239" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11240" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11241" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11242" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11243" class="mo">⊆</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11244" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11245" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11246" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11247" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11248" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11249" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11250" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11251" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11252" class="mo">(</span><span id="MathJax-Span-11253" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11254" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11255" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11256" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-512" type="math/tex">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
+ lifetime(e_3)</script>. Moreover,
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-513-Frame" class="MathJax"><nobr><span id="MathJax-Span-11257" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.998em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11258" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11259" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11261" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11262" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11263" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11264" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11265" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11266" class="mi">b</span><span id="MathJax-Span-11267" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11268" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11269" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11270" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11271" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11272" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11274" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11275" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11276" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11277" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11278" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11279" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11280" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11281" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11282" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11283" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11284" class="mi">b</span><span id="MathJax-Span-11285" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11286" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11287" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11288" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11289" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11290" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11291" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11292" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11293" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.126em; vertical-align: -0.332em;"></span></span></nobr></span><script id="MathJax-Element-513" type="math/tex">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-514-Frame" class="MathJax"><nobr><span id="MathJax-Span-11294" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.988em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11295" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11296" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11297" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11298" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11299" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11300" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11301" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11302" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11303" class="mi">b</span><span id="MathJax-Span-11304" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11305" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11306" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11307" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11308" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11310" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11312" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11313" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11314" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11315" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11316" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11317" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11318" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11319" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11320" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11321" class="mi">b</span><span id="MathJax-Span-11322" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11323" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11324" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11325" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11326" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11327" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11328" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11329" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11330" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.115em; vertical-align: -0.322em;"></span></span></nobr></span><script id="MathJax-Element-514" type="math/tex">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-515-Frame" class="MathJax"><nobr><span id="MathJax-Span-11331" class="math"><span style="display: inline-block; position: relative; width: 244px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.998em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11332" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11333" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11335" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11336" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11337" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11338" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11339" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11340" class="mi">b</span><span id="MathJax-Span-11341" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11342" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11343" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11344" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11348" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11349" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11350" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11351" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11354" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11355" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11356" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11357" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11358" class="mi">b</span><span id="MathJax-Span-11359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.717em; height: 0px;"><span style="position: absolute; clip: rect(1.743em, 1000em, 2.952em, -0.65em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11360" class="mi">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.86em; left: 0.291em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11361" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11362" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11366" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11367" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.126em; vertical-align: -0.332em;"></span></span></nobr></span><script id="MathJax-Element-515" type="math/tex">value(obj_1,attr)
+ \supseteq value(obj_3,attr)</script>. (TODO:
+ How do we know <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-516-Frame" class="MathJax"><nobr><span id="MathJax-Span-11368" class="math"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11369" class="mrow"><span id="MathJax-Span-11370" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11371" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11372" class="mn">3</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11373" class="mo">≠</span><span style="padding-left: 0.313em;" id="MathJax-Span-11374" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11375" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11376" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.004em; vertical-align: -0.234em;"></span></span></nobr></span><script id="MathJax-Element-516" type="math/tex">e_3 \neq e_1</script>? Need strict ordering on entities in semantics.)
+</p>
+</div>
+
+<div class="inference" number="20" id="specialization-alternate-inference"><div class="ruleTitle"><a href="#specialization-alternate-inference" class="internalDFN">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-517-Frame" class="MathJax"><nobr><span id="MathJax-Span-11377" class="math"><span style="display: inline-block; position: relative; width: 209px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.05em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11378" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11379" class="mtable"><span style="display: inline-block; position: relative; width: 11.857em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.503em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 11.857em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11380" class="mtd"><span id="MathJax-Span-11381" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11382" class="mi">∀</span><span id="MathJax-Span-11383" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11384" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11385" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11386" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11387" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11388" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11389" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11390" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11391" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-11392" class="mtd"><span id="MathJax-Span-11393" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11394" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11395" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11396" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11397" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11398" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11399" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11400" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11401" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11402" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11403" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11404" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11405" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11406" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11407" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11408" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11409" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11410" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11411" class="mo">(</span><span id="MathJax-Span-11412" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11413" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11414" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11415" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11416" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11417" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11418" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11419" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.053em; left: 0em;"><span id="MathJax-Span-11420" class="mtd"><span id="MathJax-Span-11421" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11422" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11423" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11425" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11427" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11428" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11429" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11430" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11431" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11432" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11433" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11434" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11435" class="mo">(</span><span id="MathJax-Span-11436" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11437" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11438" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11439" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11440" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11441" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11442" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11443" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.009em; vertical-align: -3.091em;"></span></span></nobr></span><script id="MathJax-Element-517" type="math/tex">\begin{array}[t]{l}
+\forall e_1,e_2.~
+\\
+\qquad specializationOf(e_1,e_2)
+\\
+\quad\Rightarrow
+alternateOf(e_1,e_2)
+\end{array}</script></div>
+<div class="proof">
+ <p> If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-518-Frame" class="MathJax"><nobr><span id="MathJax-Span-11444" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11445" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11446" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11447" class="mi">n</span><span id="MathJax-Span-11448" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11450" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11451" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11452" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11453" class="mo">(</span><span id="MathJax-Span-11454" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11455" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11456" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11457" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-518" type="math/tex">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-519-Frame" class="MathJax"><nobr><span id="MathJax-Span-11458" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11459" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11460" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11461" class="mi">n</span><span id="MathJax-Span-11462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11463" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11465" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11466" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11467" class="mo">(</span><span id="MathJax-Span-11468" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11469" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11470" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11471" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-519" type="math/tex">ent_2 = \rho(e_2)</script> are
+ specializations, then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-520-Frame" class="MathJax"><nobr><span id="MathJax-Span-11472" class="math"><span style="display: inline-block; position: relative; width: 212px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.488em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11473" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11475" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11476" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11477" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11478" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11479" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11480" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11481" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11483" class="mi">n</span><span id="MathJax-Span-11484" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11485" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11486" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11487" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11488" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11490" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11492" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11493" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11494" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11495" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11496" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11497" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11498" class="mi">n</span><span id="MathJax-Span-11499" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11500" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11501" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11502" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-520" type="math/tex">thingOf(ent_1) = thingOf(ent_2)</script>.
+</p>
+</div>
+
+<div class="inference" number="21" id="specialization-attributes-inference"><div class="ruleTitle"><a href="#specialization-attributes-inference" class="internalDFN">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-521-Frame" class="MathJax"><nobr><span id="MathJax-Span-11503" class="math"><span style="display: inline-block; position: relative; width: 334px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11504" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-11505" class="mtable"><span style="display: inline-block; position: relative; width: 19.159em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.495em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.159em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11506" class="mtd"><span id="MathJax-Span-11507" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11508" class="mi">∀</span><span id="MathJax-Span-11509" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11510" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11511" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11512" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11513" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11514" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11515" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11516" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11517" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11518" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11519" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11520" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11521" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11522" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-11523" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-11524" class="mtd"><span id="MathJax-Span-11525" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-11526" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11527" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11528" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11529" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11530" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11532" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11533" class="mo">(</span><span id="MathJax-Span-11534" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11535" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11536" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11537" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11538" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11540" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11541" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11542" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11543" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-11544" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-11545" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11546" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11547" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11548" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11549" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11550" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11551" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11552" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11553" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11554" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11556" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11557" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11558" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11559" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11560" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11561" class="mo">(</span><span id="MathJax-Span-11562" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11563" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11564" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11565" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11566" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11567" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11568" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11569" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: 0.046em; left: 0em;"><span id="MathJax-Span-11570" class="mtd"><span id="MathJax-Span-11571" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-11572" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11573" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11574" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11575" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11577" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11579" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11580" class="mo">(</span><span id="MathJax-Span-11581" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11582" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11583" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11584" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11585" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11586" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11587" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11588" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11589" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11590" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-521" type="math/tex">\begin{array}[t]{l}
+\forall e_1,attrs,e_2.~
+\\
+\qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
+\\
+\quad\Rightarrow
+entity(e_2,attrs)
+\end{array}</script></div>
+</section>
+<div class="proof">
+ <p> Suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-522-Frame" class="MathJax"><nobr><span id="MathJax-Span-11591" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11592" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11593" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11594" class="mi">n</span><span id="MathJax-Span-11595" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11596" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11597" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11598" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11599" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11600" class="mo">(</span><span id="MathJax-Span-11601" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11602" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11603" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11604" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-522" type="math/tex">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-523-Frame" class="MathJax"><nobr><span id="MathJax-Span-11605" class="math"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.95em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11606" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11607" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11608" class="mi">n</span><span id="MathJax-Span-11609" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11610" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11611" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11612" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11613" class="mi">ρ</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11614" class="mo">(</span><span id="MathJax-Span-11615" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11616" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11617" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11618" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-523" type="math/tex">ent_2 = \rho(e_2)</script>. Suppose
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-524-Frame" class="MathJax"><nobr><span id="MathJax-Span-11619" class="math"><span style="display: inline-block; position: relative; width: 45px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.922em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11620" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-11621" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11622" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11623" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11624" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11625" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11626" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11627" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.038em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-524" type="math/tex">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-525-Frame" class="MathJax"><nobr><span id="MathJax-Span-11628" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11629" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11630" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11633" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11634" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-525" type="math/tex">attrs</script>. Since
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-526-Frame" class="MathJax"><nobr><span id="MathJax-Span-11635" class="math"><span style="display: inline-block; position: relative; width: 105px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11636" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11637" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11638" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11639" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11640" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11641" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11642" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11643" class="mo">(</span><span id="MathJax-Span-11644" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11645" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11646" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11647" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11648" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11650" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11651" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11652" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11653" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-526" type="math/tex">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-527-Frame" class="MathJax"><nobr><span id="MathJax-Span-11654" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11655" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11656" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11657" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11658" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11660" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11661" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11662" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11663" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11664" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11665" class="mi">n</span><span id="MathJax-Span-11666" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11668" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11669" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11670" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11672" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11673" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-527" type="math/tex">v \in value(ent_1,att)</script>.
+ Thus <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-528-Frame" class="MathJax"><nobr><span id="MathJax-Span-11674" class="math"><span style="display: inline-block; position: relative; width: 133px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11675" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11676" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11677" class="mo">∈</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11678" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11679" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11680" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11681" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11682" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11683" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11684" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11685" class="mi">n</span><span id="MathJax-Span-11686" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11687" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11688" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11689" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11690" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11691" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11692" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11693" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-528" type="math/tex">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-529-Frame" class="MathJax"><nobr><span id="MathJax-Span-11694" class="math"><span style="display: inline-block; position: relative; width: 228px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.506em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11695" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11696" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11698" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11699" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11700" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11701" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11702" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11703" class="mi">n</span><span id="MathJax-Span-11704" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11705" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11706" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11707" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11708" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11709" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11711" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11712" class="mo">⊇</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11713" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11714" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11715" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11716" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11717" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11718" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11719" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11720" class="mi">n</span><span id="MathJax-Span-11721" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11722" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11723" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11724" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11725" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11726" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11727" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11728" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-529" type="math/tex">value(ent_2,att) \supseteq value(ent_1,att)</script>. Since
+ this is the case for all attribute-value pairs in <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-530-Frame" class="MathJax"><nobr><span id="MathJax-Span-11729" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.758em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11730" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11731" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11732" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11733" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11734" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11735" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.723em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-530" type="math/tex">attrs</script>, and since
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-531-Frame" class="MathJax"><nobr><span id="MathJax-Span-11736" class="math"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.428em, 1000em, 2.37em, -0.495em); top: -2.044em; left: 0em;"><span id="MathJax-Span-11737" class="mrow"><span id="MathJax-Span-11738" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11739" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11740" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.757em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-531" type="math/tex">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-532-Frame" class="MathJax"><nobr><span id="MathJax-Span-11741" class="math"><span style="display: inline-block; position: relative; width: 146px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11742" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11743" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11744" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11745" class="mi">ρ</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-11746" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-11747" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11748" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11750" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11751" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11752" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11753" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11754" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11755" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11756" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11757" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11758" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11759" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11760" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.069em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-532" type="math/tex">W,\rho \models entity(e,attrs</script>).
+ </p>
+</div>
+
+<section id="constraints">
+<h3><span class="secno">5.2 </span>Constraints</h3>
+<section id="uniqueness-constraints">
+<h4><span class="secno">5.2.1 </span>Uniqueness constraints</h4>
+
+<div class="constraint" number="22" id="key-object"><div class="ruleTitle"><a href="#key-object" class="internalDFN">Constraint 22 (key-object)</a></div>
+ <ol><li>The
+ identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-533-Frame" class="MathJax"><nobr><span id="MathJax-Span-11761" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11762" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11763" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11764" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-533" type="math/tex">id</script> is a <span class="conditional">KEY</span> for
+ the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-534-Frame" class="MathJax"><nobr><span id="MathJax-Span-11765" class="math"><span style="display: inline-block; position: relative; width: 104px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.495em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11766" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11767" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11768" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11770" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11771" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11772" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11773" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11774" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11775" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11776" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11777" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11778" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11779" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11780" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11781" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11782" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-534" type="math/tex">entity(id,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-535-Frame" class="MathJax"><nobr><span id="MathJax-Span-11783" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11784" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11785" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11786" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-535" type="math/tex">id</script>
+ is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-536-Frame" class="MathJax"><nobr><span id="MathJax-Span-11787" class="math"><span style="display: inline-block; position: relative; width: 155px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11788" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11789" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11790" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11792" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11793" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11794" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11796" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11797" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11798" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11799" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11800" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11801" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11803" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11804" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11805" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11807" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11808" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11809" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11810" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11811" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11812" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11813" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11814" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-536" type="math/tex">activity(id,t_1,t_2,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-537-Frame" class="MathJax"><nobr><span id="MathJax-Span-11815" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11816" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11818" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-537" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-538-Frame" class="MathJax"><nobr><span id="MathJax-Span-11819" class="math"><span style="display: inline-block; position: relative; width: 103px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11820" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11822" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11823" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11826" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11827" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11828" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11829" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11830" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11832" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11833" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11834" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11835" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-538" type="math/tex">agent(id,attrs)</script> statement.</li></ol></div>
+<div class="constraint" number="23" id="key-properties"><div class="ruleTitle"><a href="#key-properties" class="internalDFN">Constraint 23 (key-properties)</a></div>
+ <ol><li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-539-Frame" class="MathJax"><nobr><span id="MathJax-Span-11836" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11837" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11838" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11839" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-539" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-540-Frame" class="MathJax"><nobr><span id="MathJax-Span-11840" class="math"><span style="display: inline-block; position: relative; width: 227px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11841" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11842" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11843" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11844" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11845" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11846" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11847" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11848" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11849" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11850" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11852" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11853" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11854" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11855" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11856" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11857" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11858" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11859" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11860" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11861" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11862" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11863" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11864" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11865" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11866" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11867" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11869" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11870" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11871" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-540" type="math/tex">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-541-Frame" class="MathJax"><nobr><span id="MathJax-Span-11872" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11873" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11874" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11875" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-541" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-542-Frame" class="MathJax"><nobr><span id="MathJax-Span-11876" class="math"><span style="display: inline-block; position: relative; width: 141px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11877" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11878" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11879" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11880" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11881" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11882" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11883" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11884" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11886" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11887" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11888" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11889" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11890" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11891" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11892" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11894" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11895" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11896" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11897" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.045em; vertical-align: -0.252em;"></span></span></nobr></span><script id="MathJax-Element-542" type="math/tex">used(id,a,e,t,attrs)</script>
+ statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-543-Frame" class="MathJax"><nobr><span id="MathJax-Span-11898" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11899" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11900" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11901" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-543" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-544-Frame" class="MathJax"><nobr><span id="MathJax-Span-11902" class="math"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11903" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11904" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11905" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11906" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11907" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11908" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11909" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11910" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11911" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11912" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11913" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11914" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11915" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11916" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11917" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11918" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11919" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11920" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11921" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11922" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11923" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11924" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11925" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11926" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11927" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11928" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11929" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11930" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11931" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11933" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11934" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-544" type="math/tex">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-545-Frame" class="MathJax"><nobr><span id="MathJax-Span-11935" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11936" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11937" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11938" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-545" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-546-Frame" class="MathJax"><nobr><span id="MathJax-Span-11939" class="math"><span style="display: inline-block; position: relative; width: 236px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11940" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11941" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11942" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11943" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11944" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11945" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11946" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11947" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11949" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11950" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11951" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11952" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11953" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11954" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11955" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11956" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11957" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11958" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11959" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11960" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11961" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11962" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11964" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11966" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11967" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11968" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11970" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11972" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11973" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11974" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-546" type="math/tex">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-547-Frame" class="MathJax"><nobr><span id="MathJax-Span-11975" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11976" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11978" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-547" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-548-Frame" class="MathJax"><nobr><span id="MathJax-Span-11979" class="math"><span style="display: inline-block; position: relative; width: 230px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-11980" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11981" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11982" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11983" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11984" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11985" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11986" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11987" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11988" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11989" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11990" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-11991" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11992" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11993" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11994" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-11995" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11996" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-11997" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-11998" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-11999" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12000" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12002" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12003" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12004" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12005" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12006" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12007" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12009" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12010" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12011" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12012" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-548" type="math/tex">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-549-Frame" class="MathJax"><nobr><span id="MathJax-Span-12013" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12014" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12015" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12016" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-549" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-550-Frame" class="MathJax"><nobr><span id="MathJax-Span-12017" class="math"><span style="display: inline-block; position: relative; width: 233px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12018" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12019" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12021" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12022" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12023" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12024" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12025" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12026" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12027" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12028" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12029" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12030" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12031" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12032" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12033" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12034" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12035" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12036" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12037" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12038" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12039" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12040" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12041" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12043" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12044" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12045" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12046" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12047" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12048" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12049" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12050" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-550" type="math/tex">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-551-Frame" class="MathJax"><nobr><span id="MathJax-Span-12051" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12052" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12053" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12054" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-551" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-552-Frame" class="MathJax"><nobr><span id="MathJax-Span-12055" class="math"><span style="display: inline-block; position: relative; width: 295px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12056" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12057" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12058" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12059" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12060" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12061" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12063" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12064" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12065" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12066" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12067" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12068" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12069" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12070" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12071" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12072" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12073" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12074" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12075" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12076" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12077" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12078" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12080" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12081" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12083" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12084" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12086" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12088" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12090" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12091" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12092" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12093" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12094" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12096" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12097" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12098" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-552" type="math/tex">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-553-Frame" class="MathJax"><nobr><span id="MathJax-Span-12099" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12100" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12101" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12102" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-553" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-554-Frame" class="MathJax"><nobr><span id="MathJax-Span-12103" class="math"><span style="display: inline-block; position: relative; width: 222px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12104" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12105" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12107" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12108" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12109" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12111" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12112" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12113" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12114" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12115" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12116" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12117" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12118" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12119" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12120" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12121" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12122" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12123" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12124" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12126" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12127" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12128" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12129" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12130" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12131" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12132" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12133" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12134" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-554" type="math/tex">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-555-Frame" class="MathJax"><nobr><span id="MathJax-Span-12135" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12136" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12137" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12138" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-555" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-556-Frame" class="MathJax"><nobr><span id="MathJax-Span-12139" class="math"><span style="display: inline-block; position: relative; width: 262px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12140" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12141" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12142" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12143" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12144" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12145" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12146" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12147" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12148" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12149" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12150" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12152" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12153" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12154" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12155" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12156" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12157" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12158" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12159" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12160" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12161" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12162" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12163" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12164" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12165" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12166" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12167" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12168" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12169" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12173" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12174" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12175" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.076em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-556" type="math/tex">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-557-Frame" class="MathJax"><nobr><span id="MathJax-Span-12176" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12177" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12178" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12179" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-557" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-558-Frame" class="MathJax"><nobr><span id="MathJax-Span-12180" class="math"><span style="display: inline-block; position: relative; width: 272px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12181" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12182" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12183" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12184" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12185" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12186" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12187" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12188" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12189" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12190" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12191" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12192" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12193" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12194" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12195" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12196" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12197" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12198" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12199" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12200" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12201" class="mi">a</span><span id="MathJax-Span-12202" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12203" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12204" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12205" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12206" class="mi">a</span><span id="MathJax-Span-12207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12208" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12209" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12211" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12212" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12213" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12214" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12215" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12216" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12217" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12218" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.114em; vertical-align: -0.321em;"></span></span></nobr></span><script id="MathJax-Element-558" type="math/tex">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
+ <li>The identifier field <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-559-Frame" class="MathJax"><nobr><span id="MathJax-Span-12219" class="math"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.477em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12220" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12221" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12222" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.87em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-559" type="math/tex">id</script> is a <span class="conditional">KEY</span> for the
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-560-Frame" class="MathJax"><nobr><span id="MathJax-Span-12223" class="math"><span style="display: inline-block; position: relative; width: 235px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12224" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12225" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12226" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12227" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12228" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12229" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12230" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12231" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12232" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12233" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12234" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12235" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12237" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12238" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12239" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12240" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12241" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12243" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12244" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12245" class="mn">2</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12246" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12247" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12248" class="mn">1</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12249" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12250" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12251" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12252" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12253" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12254" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12255" class="mo">)</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-560" type="math/tex">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
+ </div>
+<div class="constraint" number="24" id="unique-generation"><div class="ruleTitle"><a href="#unique-generation" class="internalDFN">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-561-Frame" class="MathJax"><nobr><span id="MathJax-Span-12256" class="math"><span style="display: inline-block; position: relative; width: 582px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.972em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12257" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12258" class="mtable"><span style="display: inline-block; position: relative; width: 33.645em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.366em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.645em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12259" class="mtd"><span id="MathJax-Span-12260" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12261" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12262" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12263" class="mi">e</span><span id="MathJax-Span-12264" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12265" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12266" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12268" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12269" class="mi">e</span><span id="MathJax-Span-12270" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12271" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12272" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12273" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12274" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12276" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12277" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12280" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12281" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12284" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12285" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12286" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12288" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12289" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12290" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12291" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12292" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12293" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12294" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12297" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12298" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12299" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12300" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12301" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12302" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-12303" class="mtd"><span id="MathJax-Span-12304" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12305" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12306" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12307" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12308" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12309" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12311" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12312" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12313" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12314" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12316" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12318" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12319" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12321" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12322" class="mi">e</span><span id="MathJax-Span-12323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12324" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12326" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12327" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12328" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12329" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12330" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12331" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12332" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12333" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12334" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12338" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12339" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12340" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12341" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12342" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12343" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12344" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12346" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12347" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12348" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12349" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12350" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12351" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12353" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12354" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12355" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12356" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12357" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12358" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12359" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12360" class="mi">e</span><span id="MathJax-Span-12361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12362" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12363" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12364" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12365" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12367" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12368" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12369" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12371" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12378" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12380" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.951em, -0.526em); top: -0.024em; left: 0em;"><span id="MathJax-Span-12381" class="mtd"><span id="MathJax-Span-12382" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12383" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12384" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12385" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12386" class="mi">e</span><span id="MathJax-Span-12387" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12388" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12389" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12390" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12391" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12392" class="mi">e</span><span id="MathJax-Span-12393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12394" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12395" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.926em; vertical-align: -3.007em;"></span></span></nobr></span><script id="MathJax-Element-561" type="math/tex">\begin{array}[t]{l}
+\forall gen_1,gen_2,e,a,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen_1,e,a,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 = gen_2
+\end{array}</script></div>
+<div class="constraint" number="25" id="unique-invalidation"><div class="ruleTitle"><a href="#unique-invalidation" class="internalDFN">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-562-Frame" class="MathJax"><nobr><span id="MathJax-Span-12396" class="math"><span style="display: inline-block; position: relative; width: 588px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12397" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12398" class="mtable"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.299em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12399" class="mtd"><span id="MathJax-Span-12400" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12401" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12402" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12403" class="mi">n</span><span id="MathJax-Span-12404" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12405" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12406" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12407" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12408" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12409" class="mi">n</span><span id="MathJax-Span-12410" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12411" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12412" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12413" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12414" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12415" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12416" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12417" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12418" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12419" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12420" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12421" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12422" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12424" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12425" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12426" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12427" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12429" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12430" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12431" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12432" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12433" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12434" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12435" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12437" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12438" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12439" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12440" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12441" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12442" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-12443" class="mtd"><span id="MathJax-Span-12444" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12445" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12446" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12447" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12448" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12449" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12450" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12451" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12452" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12453" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12454" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12455" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12456" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12457" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12458" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12459" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12460" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12461" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12462" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12463" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12464" class="mi">n</span><span id="MathJax-Span-12465" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12466" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12467" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12468" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12469" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12470" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12471" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12472" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12473" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12475" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12476" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12477" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12478" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12480" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12481" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12482" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12483" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12484" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12485" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12486" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12487" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12488" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12489" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12490" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12491" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12492" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12493" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12494" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12495" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12496" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12497" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12498" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12499" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12500" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12501" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12502" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12503" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12504" class="mi">n</span><span id="MathJax-Span-12505" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12506" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12507" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12508" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12509" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12511" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12512" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12513" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12514" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12515" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12516" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12517" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12518" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12519" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12520" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12522" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12523" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12524" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-12525" class="mtd"><span id="MathJax-Span-12526" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12527" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12528" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12529" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12530" class="mi">n</span><span id="MathJax-Span-12531" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12532" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12533" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12534" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12535" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12536" class="mi">n</span><span id="MathJax-Span-12537" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12538" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12539" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-562" type="math/tex">\begin{array}[t]{l}
+\forall inv_1,inv_2,e,a,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasInvalidatedBy(inv_1,e,a,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a,t_2,attrs_2)
+\\
+\quad\Rightarrow
+inv_1 = inv_2
+\end{array}</script></div>
+<div class="constraint" number="26" id="unique-wasStartedBy"><div class="ruleTitle"><a href="#unique-wasStartedBy" class="internalDFN">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-563-Frame" class="MathJax"><nobr><span id="MathJax-Span-12540" class="math"><span style="display: inline-block; position: relative; width: 615px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.92em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12541" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12542" class="mtable"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.148em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12543" class="mtd"><span id="MathJax-Span-12544" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12545" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12546" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12548" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12549" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12550" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12551" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12552" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12553" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12554" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12555" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12556" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12557" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12558" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12559" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12560" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12561" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12562" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12563" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12564" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12565" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12566" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12567" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12568" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12569" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12570" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12574" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12578" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12579" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12580" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12582" class="mn">2</span><span style="display: inline-block; width: 0px; 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top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12628" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12629" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12630" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12632" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12633" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12634" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12635" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12637" class="mn">1</span><span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12658" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12659" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12660" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12661" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12663" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12664" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12665" class="msubsup"><span style="display: inline-block; 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width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12693" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12694" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12695" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12696" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12697" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12698" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12699" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12700" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12701" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12702" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12703" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12704" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12705" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12706" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12707" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12709" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.87em; vertical-align: -2.951em;"></span></span></nobr></span><script id="MathJax-Element-563" type="math/tex">\begin{array}[t]{l}
+\forall start_1,start_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start_1,a,e_1,a_0,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_0,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 = start_2
+\end{array}</script></div>
+<div class="constraint" number="27" id="unique-wasEndedBy"><div class="ruleTitle"><a href="#unique-wasEndedBy" class="internalDFN">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-564-Frame" class="MathJax"><nobr><span id="MathJax-Span-12710" class="math"><span style="display: inline-block; position: relative; width: 589px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.052em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12711" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12712" class="mtable"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.396em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.905em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12713" class="mtd"><span id="MathJax-Span-12714" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12715" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12716" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12717" class="mi">n</span><span id="MathJax-Span-12718" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12719" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12720" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12721" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12722" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12723" class="mi">n</span><span id="MathJax-Span-12724" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12725" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12726" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12727" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12728" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12729" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12730" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12731" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12732" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12733" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12734" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12735" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12736" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12737" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12738" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12739" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12740" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12741" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12742" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12743" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12744" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12745" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12746" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12747" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12748" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12749" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12750" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12751" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12752" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12753" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12754" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12755" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12756" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12757" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12758" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12759" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12760" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12761" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12762" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12763" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12764" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12765" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12766" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.277em; left: 0em;"><span id="MathJax-Span-12767" class="mtd"><span id="MathJax-Span-12768" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12769" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12770" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12771" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12772" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12773" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12774" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12775" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12776" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12777" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12778" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12779" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12780" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12781" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12782" class="mi">n</span><span id="MathJax-Span-12783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12784" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12785" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12786" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12787" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12788" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12789" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12790" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12791" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12792" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12793" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12794" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12795" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12796" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12797" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12798" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12800" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12801" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12803" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12804" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12805" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12806" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12807" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12808" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12809" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12810" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12811" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12812" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12813" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12814" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12815" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12816" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12817" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12818" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12819" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12820" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12822" class="mi">n</span><span id="MathJax-Span-12823" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12824" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12825" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12826" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12827" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12828" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12829" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12830" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12831" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12832" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12833" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12834" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12835" class="mn">0</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12836" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12837" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12838" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12839" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12840" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12841" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12842" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12844" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12845" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12846" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12847" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12848" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.062em; left: 0em;"><span id="MathJax-Span-12849" class="mtd"><span id="MathJax-Span-12850" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12851" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12852" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12853" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12854" class="mi">n</span><span id="MathJax-Span-12855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12856" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12857" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12858" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12859" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12860" class="mi">n</span><span id="MathJax-Span-12861" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12862" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12863" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.011em; vertical-align: -3.093em;"></span></span></nobr></span><script id="MathJax-Element-564" type="math/tex">\begin{array}[t]{l}
+\forall end_1,end_2,a,e_1,e_2,a_0,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasEndedBy(end_1,a,e_1,a_0,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_0,t_2,attrs_2)
+\\
+\quad\Rightarrow
+end_1 = end_2
+\end{array}</script></div>
+<div class="constraint" number="28" id="unique-startTime"><div class="ruleTitle"><a href="#unique-startTime" class="internalDFN">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-565-Frame" class="MathJax"><nobr><span id="MathJax-Span-12864" class="math"><span style="display: inline-block; position: relative; width: 483px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.91em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12865" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12866" class="mtable"><span style="display: inline-block; position: relative; width: 27.862em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.138em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.862em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12867" class="mtd"><span id="MathJax-Span-12868" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12869" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12870" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12871" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12872" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12873" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12874" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12875" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12876" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12877" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12878" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12879" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12880" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12881" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12882" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12883" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12885" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12886" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12887" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12888" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12889" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12890" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12891" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12892" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12893" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12894" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12895" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12896" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12897" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12898" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12899" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12900" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12901" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12902" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12905" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12906" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12907" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12908" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12909" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-12910" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-12911" class="mtd"><span id="MathJax-Span-12912" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-12913" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12914" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12915" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12917" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12918" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12919" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12920" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12921" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12922" class="mo">(</span><span id="MathJax-Span-12923" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12924" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12925" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12926" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12927" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12928" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12929" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12930" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12931" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12932" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12933" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12934" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12935" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12936" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12939" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12940" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-12941" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-12942" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12943" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12944" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12945" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12946" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12947" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12948" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12949" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12950" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12951" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12952" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12953" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12954" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12955" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12957" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12958" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12959" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12960" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12962" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12963" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12964" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12965" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-12966" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-12967" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12968" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12969" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12970" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12972" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-12973" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12974" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12975" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12976" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-12977" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12978" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12979" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12980" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.895em, -0.526em); top: -0.08em; left: 0em;"><span id="MathJax-Span-12981" class="mtd"><span id="MathJax-Span-12982" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-12983" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12984" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-12985" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12986" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12987" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-12988" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-12989" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.859em; vertical-align: -2.941em;"></span></span></nobr></span><script id="MathJax-Element-565" type="math/tex">\begin{array}[t]{l}
+\forall start,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
+\\
+\qquad activity(a_2,t_1,t_2,attrs) \wedge wasStartedBy(start,a_2,e,a_1,t,attrs_1)
+\\
+\quad\Rightarrow
+t_1 = t
+\end{array}</script></div>
+<div class="constraint" number="29" id="unique-endTime"><div class="ruleTitle"><a href="#unique-endTime" class="internalDFN">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-566-Frame" class="MathJax"><nobr><span id="MathJax-Span-12990" class="math"><span style="display: inline-block; position: relative; width: 470px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.91em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-12991" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-12992" class="mtable"><span style="display: inline-block; position: relative; width: 27.103em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.138em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.103em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-12993" class="mtd"><span id="MathJax-Span-12994" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-12995" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12996" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12997" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-12998" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-12999" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13000" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13001" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13002" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13003" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13004" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13005" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13006" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13007" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13008" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13009" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13010" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13011" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13012" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13013" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13014" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13016" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13017" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13018" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13019" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13020" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13021" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13022" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13023" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13024" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13025" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13026" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13027" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13028" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13029" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13030" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13031" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13032" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13033" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13034" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13035" class="mtd"><span id="MathJax-Span-13036" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13037" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13038" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13039" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13041" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13042" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13045" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13046" class="mo">(</span><span id="MathJax-Span-13047" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13048" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13049" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13050" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13051" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13053" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13054" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13056" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13057" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13058" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13059" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13063" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13064" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13065" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13066" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13067" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13068" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13069" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13070" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13071" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13073" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13074" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13075" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13076" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13077" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13078" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13079" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13080" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13081" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13082" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13083" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13084" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13085" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13086" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13087" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13088" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13089" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13090" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13091" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13092" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13093" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13094" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13095" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13096" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13097" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13098" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13099" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13100" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.895em, -0.526em); top: -0.08em; left: 0em;"><span id="MathJax-Span-13101" class="mtd"><span id="MathJax-Span-13102" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13103" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13104" class="mo">⇒</span><span style="padding-left: 0.313em;" id="MathJax-Span-13105" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13106" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13107" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13108" class="mo">=</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13109" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.859em; vertical-align: -2.941em;"></span></span></nobr></span><script id="MathJax-Element-566" type="math/tex">\begin{array}[t]{l}
+\forall end,a_1,a_2,t,t_1,t_2,e,attrs,attrs_1.~
+\\
+\qquad activity(a_2,t_1,t_2,attrs) \wedge wasEndedBy(end,a_2,e,a_1,t,attrs_1)
+\\
+\quad\Rightarrow
+t_2 = t
+\end{array}</script></div>
+</section>
+
+<section id="ordering-constraints">
+<h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
+
+
+<div class="constraint" number="30" id="start-precedes-end"><div class="ruleTitle"><a href="#start-precedes-end" class="internalDFN">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-567-Frame" class="MathJax"><nobr><span id="MathJax-Span-13110" class="math"><span style="display: inline-block; position: relative; width: 588px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13111" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13112" class="mtable"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.995em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13113" class="mtd"><span id="MathJax-Span-13114" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13115" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13116" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13117" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13118" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13119" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13120" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13121" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13122" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13123" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13124" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13125" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13126" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13127" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13128" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13129" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13130" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13131" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13132" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13133" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13134" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13135" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13137" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13139" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13140" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13141" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13142" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13143" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13144" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13145" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13146" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13147" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13148" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13150" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13151" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13152" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13153" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13154" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13155" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13157" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13158" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13159" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13160" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13161" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13162" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13163" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13164" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13165" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13166" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13167" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13168" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13169" class="mtd"><span id="MathJax-Span-13170" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13171" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13172" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13174" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13175" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13176" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13177" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13178" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13179" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13180" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13181" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13182" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13183" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13184" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13185" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13186" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13187" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13188" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13189" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13190" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13191" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13192" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13194" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13195" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13196" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13197" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13198" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13199" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13200" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13201" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13202" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13203" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13204" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13205" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13206" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13208" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13209" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13210" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13211" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13212" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13213" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13214" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13215" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13216" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13217" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13218" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13219" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13220" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13221" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13222" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13223" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13224" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13225" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13226" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13227" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13228" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13229" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13230" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13231" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13232" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13233" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13234" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13235" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13236" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13237" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13238" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13239" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13240" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13241" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13242" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13246" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13247" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13248" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13249" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13250" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13251" class="mtd"><span id="MathJax-Span-13252" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13253" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13254" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13255" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13256" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13257" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13258" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13259" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13260" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13261" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13262" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13263" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-567" type="math/tex">\begin{array}[t]{l}
+\forall start,end,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start \preceq end
+\end{array}</script></div>
+<div class="constraint" number="31" id="start-start-ordering"><div class="ruleTitle"><a href="#start-start-ordering" class="internalDFN">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-568-Frame" class="MathJax"><nobr><span id="MathJax-Span-13264" class="math"><span style="display: inline-block; position: relative; width: 615px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.968em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13265" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13266" class="mtable"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.254em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 35.572em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13267" class="mtd"><span id="MathJax-Span-13268" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13269" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13270" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13272" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13273" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13274" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13275" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13276" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13278" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13279" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13280" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13281" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13284" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13285" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13286" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13287" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13288" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13289" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13290" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13291" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13292" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13293" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13294" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13295" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13296" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13297" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13298" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13299" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13300" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13301" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13302" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13303" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13304" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13306" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13307" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13308" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13310" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13311" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13312" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13313" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13314" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13315" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13316" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13317" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13318" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13319" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13320" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13321" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13323" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13324" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13325" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13326" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13327" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13328" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13329" class="mtd"><span id="MathJax-Span-13330" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13331" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13332" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13333" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13334" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13335" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13337" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13338" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13339" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13340" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13341" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13342" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13343" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13345" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13347" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13348" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13349" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13350" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13351" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13352" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13353" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13354" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13355" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13356" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13357" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13358" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13360" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13361" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13362" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13363" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13365" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13367" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13368" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13369" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13370" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13371" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13372" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13373" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13374" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13375" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13376" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13377" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13378" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13379" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13380" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13381" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13382" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13386" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13387" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13388" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13389" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13391" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13392" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13394" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13395" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13396" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13397" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13398" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13399" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13400" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13401" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13402" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13403" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13404" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13405" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13406" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13407" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13408" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13409" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13410" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13411" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13414" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13415" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13416" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13417" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13418" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.895em, -0.526em); top: -0.022em; left: 0em;"><span id="MathJax-Span-13419" class="mtd"><span id="MathJax-Span-13420" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13421" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13422" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13423" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13424" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13425" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13426" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13427" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13428" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13429" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13430" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13431" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13433" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13434" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13437" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.921em; vertical-align: -3.003em;"></span></span></nobr></span><script id="MathJax-Element-568" type="math/tex">\begin{array}[t]{l}
+\forall start_1,start_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasStartedBy(start_2,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq start_2
+\end{array}</script></div>
+<div class="constraint" number="32" id="end-end-ordering"><div class="ruleTitle"><a href="#end-end-ordering" class="internalDFN">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-569-Frame" class="MathJax"><nobr><span id="MathJax-Span-13438" class="math"><span style="display: inline-block; position: relative; width: 589px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13439" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13440" class="mtable"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.386em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.054em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13441" class="mtd"><span id="MathJax-Span-13442" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13443" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13444" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13445" class="mi">n</span><span id="MathJax-Span-13446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13447" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13448" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13450" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13451" class="mi">n</span><span id="MathJax-Span-13452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13456" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13459" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13463" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13467" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13468" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13471" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13473" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13474" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13476" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13477" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13480" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13484" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13485" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13486" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13487" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13488" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13489" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13490" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13491" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13492" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13493" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13494" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13495" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13496" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13497" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13498" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13499" class="mtd"><span id="MathJax-Span-13500" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13501" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13502" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13504" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13505" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13506" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13507" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13508" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13509" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13510" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13511" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13512" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13513" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13514" class="mi">n</span><span id="MathJax-Span-13515" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13516" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13517" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13518" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13519" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13520" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13522" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13523" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13524" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13525" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13526" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13527" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13528" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13529" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13531" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13533" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13535" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13536" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13537" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13538" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13539" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13540" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13541" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13542" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13543" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13544" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13545" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13546" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13547" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13548" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13550" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13551" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13552" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13554" class="mi">n</span><span id="MathJax-Span-13555" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13556" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13557" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13558" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13559" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13560" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13561" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13562" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13563" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13564" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13565" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13566" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13567" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13568" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13569" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13570" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13571" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13572" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13573" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13574" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13576" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13577" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13578" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13579" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13580" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13581" class="mtd"><span id="MathJax-Span-13582" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13583" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13584" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13585" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13586" class="mi">n</span><span id="MathJax-Span-13587" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13588" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13589" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13590" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13592" class="mi">n</span><span id="MathJax-Span-13593" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13594" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13595" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-569" type="math/tex">\begin{array}[t]{l}
+\forall end_1,end_2,a,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasEndedBy(end_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+end_1 \preceq end_2
+\end{array}</script></div>
+<div class="constraint" number="33" id="usage-within-activity"><div class="ruleTitle"><a href="#usage-within-activity" class="internalDFN">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-570-Frame" class="MathJax"><nobr><span id="MathJax-Span-13596" class="math"><span style="display: inline-block; position: relative; width: 505px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.968em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13597" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13598" class="mtable"><span style="display: inline-block; position: relative; width: 29.147em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.149em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 29.147em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13599" class="mtd"><span id="MathJax-Span-13600" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13601" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13602" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13604" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13605" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13606" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13607" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13608" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13609" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13610" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13611" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13612" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13613" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13614" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13615" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13616" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13617" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13618" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13619" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13620" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13621" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13622" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13623" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13624" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13625" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13626" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13627" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13628" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13629" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13630" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13631" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13632" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13633" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13634" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13636" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13637" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13638" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13639" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13640" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13641" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13642" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13643" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13644" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13645" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13646" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13647" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13648" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13649" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13650" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13651" class="mtd"><span id="MathJax-Span-13652" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13653" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13654" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13655" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13656" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13657" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13659" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13661" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13662" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13663" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13664" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13665" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13666" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13667" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13669" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13670" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13671" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13672" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13673" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13674" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13675" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13676" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13677" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13678" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13679" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13680" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13681" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13682" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13683" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13685" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13686" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13687" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13688" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13689" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13690" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13691" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13692" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13693" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13694" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13695" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13696" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13697" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13698" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13699" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13700" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13701" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13702" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13703" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13704" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13705" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13706" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13707" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13708" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13709" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13710" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13711" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13713" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13714" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13715" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13717" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13718" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13719" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13720" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13721" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13722" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.848em, -0.526em); top: -0.022em; left: 0em;"><span id="MathJax-Span-13723" class="mtd"><span id="MathJax-Span-13724" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13725" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13726" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13727" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13728" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13729" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13730" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13731" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13732" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13733" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13734" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13735" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.921em; vertical-align: -3.003em;"></span></span></nobr></span><script id="MathJax-Element-570" type="math/tex">\begin{array}[t]{l}
+\forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge used(use,a,e_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start \preceq use
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-571-Frame" class="MathJax"><nobr><span id="MathJax-Span-13736" class="math"><span style="display: inline-block; position: relative; width: 491px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13737" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13738" class="mtable"><span style="display: inline-block; position: relative; width: 28.329em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.329em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13739" class="mtd"><span id="MathJax-Span-13740" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13741" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13742" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13743" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13744" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13745" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13746" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13747" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13748" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13749" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13750" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13751" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13752" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13753" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13754" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13755" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13757" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13758" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13759" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13760" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13761" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13762" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13763" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13764" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13765" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13766" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13767" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13768" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13769" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13770" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13771" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13772" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13773" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13774" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13775" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13776" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13777" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13778" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13779" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13780" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13782" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13783" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13784" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13785" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13786" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13787" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13788" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-13789" class="mtd"><span id="MathJax-Span-13790" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13791" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13792" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13793" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13794" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13795" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13796" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13797" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13798" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13799" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13800" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13801" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13802" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13804" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13805" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13806" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13809" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13810" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13811" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13812" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13813" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13814" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13815" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13816" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13817" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13818" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13819" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13820" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13821" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13822" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13823" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13824" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13825" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13826" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13827" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13828" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13829" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13830" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13831" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13832" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13833" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13834" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13835" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13836" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13837" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13838" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13839" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13840" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13841" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13842" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13843" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13844" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13845" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13846" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13847" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13848" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13849" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13850" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13851" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13852" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13853" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13854" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13855" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13856" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-13857" class="mtd"><span id="MathJax-Span-13858" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-13859" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13860" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13861" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13862" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13863" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-13864" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-13865" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13866" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13867" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-571" type="math/tex">\begin{array}[t]{l}
+\forall use,end,a,e_1,e_2,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad used(use,a,e_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+use \preceq end
+\end{array}</script></li></ol></div>
+<div class="constraint" number="34" id="generation-within-activity"><div class="ruleTitle"><a href="#generation-within-activity" class="internalDFN">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-572-Frame" class="MathJax"><nobr><span id="MathJax-Span-13868" class="math"><span style="display: inline-block; position: relative; width: 592px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-13869" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-13870" class="mtable"><span style="display: inline-block; position: relative; width: 34.229em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.229em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-13871" class="mtd"><span id="MathJax-Span-13872" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-13873" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13874" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13875" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13876" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13877" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13878" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13879" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13880" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13881" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13882" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13883" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13884" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13885" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13886" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13887" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13889" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13890" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13891" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13892" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13893" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13894" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13895" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13896" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13897" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13898" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13899" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13900" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13901" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13902" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13903" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13904" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13905" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13906" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13907" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13908" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13909" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13910" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13911" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13912" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13913" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13914" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13915" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13916" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13917" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13918" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13919" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13920" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13921" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-13922" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-13923" class="mtd"><span id="MathJax-Span-13924" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-13925" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13926" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13927" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13928" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13929" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13930" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13931" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13932" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13933" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13934" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13935" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13936" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13937" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13938" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13939" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13941" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13942" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13943" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13944" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13945" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13946" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13948" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13950" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13951" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13952" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13953" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13954" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13955" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13956" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13957" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13958" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13959" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13960" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13961" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13962" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-13963" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13964" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13965" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13966" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-13967" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-13968" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13969" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13970" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13971" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13973" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13974" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13975" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13976" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13977" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13978" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13979" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13980" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13981" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13982" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13983" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13984" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13985" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13986" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13987" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13988" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13989" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13991" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-13992" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-13993" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13994" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-13995" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-13996" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-13997" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14000" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14002" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14003" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14004" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14005" class="mtd"><span id="MathJax-Span-14006" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14007" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14008" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14009" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14010" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14011" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14012" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14013" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14014" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14015" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14016" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14017" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-572" type="math/tex">\begin{array}[t]{l}
+\forall start,gen,e_1,e_2,a,a_1,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start,a,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen,e_2,a,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start \preceq gen
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-573-Frame" class="MathJax"><nobr><span id="MathJax-Span-14018" class="math"><span style="display: inline-block; position: relative; width: 557px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14019" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14020" class="mtable"><span style="display: inline-block; position: relative; width: 32.185em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 32.185em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14021" class="mtd"><span id="MathJax-Span-14022" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14023" class="mi">∀</span><span style="font-family: STIXGeneral; 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position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14035" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14036" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14037" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14038" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14039" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14040" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14041" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14042" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14043" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14045" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14046" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14047" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14048" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14049" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14050" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14051" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14052" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14053" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14054" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14055" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14056" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14057" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14058" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14059" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14060" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14061" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14062" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14063" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14064" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14065" class="mtd"><span id="MathJax-Span-14066" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14067" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14068" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14069" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14070" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14071" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14073" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14075" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14076" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14077" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14078" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14079" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14080" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14081" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14082" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14083" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14084" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14085" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14086" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14087" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14088" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14089" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14090" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; 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padding-left: 0.25em;" id="MathJax-Span-14099" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14100" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14101" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14102" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14103" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14104" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14105" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14106" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14107" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14108" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14109" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14110" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14111" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14112" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14113" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14114" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14115" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14116" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14117" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14118" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14119" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14120" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14121" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14122" class="mi">a</span><span style="display: inline-block; 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font-family: STIXGeneral;" id="MathJax-Span-14127" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14128" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14129" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14130" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14131" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14132" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14133" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14134" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14135" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14136" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-14137" class="mtd"><span id="MathJax-Span-14138" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14139" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14140" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14141" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14142" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14143" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14144" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14145" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14146" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14147" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-573" type="math/tex">\begin{array}[t]{l}
+\forall gen,end,e,e_1,a,a_1,t,t_1,attrs,attrs_1.~
+\\
+\qquad wasGeneratedBy(gen,e,a,t,attrs) \wedge wasEndedBy(end,a,e_1,a_1,t_1,attrs_1)
+\\
+\quad\Rightarrow
+gen \preceq end
+\end{array}</script></li></ol></div>
+<div class="constraint" number="35" id="wasInformedBy-ordering"><div class="ruleTitle"><a href="#wasInformedBy-ordering" class="internalDFN">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-574-Frame" class="MathJax"><nobr><span id="MathJax-Span-14148" class="math"><span style="display: inline-block; position: relative; width: 847px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.354em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14149" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14150" class="mtable"><span style="display: inline-block; position: relative; width: 49.124em; height: 0px;"><span style="position: absolute; clip: rect(3.89em, 1000em, 8.002em, -0.526em); top: -4.79em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.124em; height: 0px;"><span style="position: absolute; clip: rect(1.671em, 1000em, 3.059em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14151" class="mtd"><span id="MathJax-Span-14152" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14153" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14154" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14155" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14156" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14157" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14158" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14159" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14160" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14161" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14162" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14163" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14164" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14165" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14166" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14167" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14168" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14169" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14170" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14171" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14172" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14173" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.447em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14174" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14175" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14176" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14177" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14178" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14179" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14180" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14181" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14182" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.505em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14183" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14184" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14185" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14186" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14187" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14188" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14189" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14190" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14191" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14192" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14194" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14195" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14196" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14197" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14199" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14200" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14201" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14202" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14203" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14204" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14205" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14206" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14207" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14209" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14210" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14211" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14212" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14213" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14214" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14215" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14216" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14217" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14218" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14219" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14220" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14221" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14222" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14223" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.671em, 1000em, 3.059em, -0.526em); top: -1.082em; left: 0em;"><span id="MathJax-Span-14224" class="mtd"><span id="MathJax-Span-14225" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14226" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14227" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14228" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14229" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14230" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14231" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14232" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14233" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14234" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14235" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14236" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14237" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14238" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14239" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14240" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14241" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14242" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14243" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14244" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14245" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14246" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14247" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14248" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14249" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14250" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14251" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14252" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14253" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14254" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14255" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14256" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14257" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14258" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14259" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14260" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14261" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14262" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14263" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14264" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14265" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14267" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14268" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14269" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14270" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14271" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14272" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14274" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14275" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14276" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14277" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14278" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14279" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14280" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14281" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14282" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14283" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14284" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14285" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14286" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14287" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14288" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.447em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14289" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14290" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14291" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14292" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14293" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14294" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14295" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14296" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14297" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14298" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14299" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14300" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14301" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14302" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14303" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14304" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14305" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14306" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14307" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14308" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14309" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14310" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14311" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14312" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14313" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14314" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14315" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14316" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14318" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14319" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14320" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14321" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14322" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14323" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14324" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14325" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14326" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14327" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14328" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.528em, 1000em, 2.258em, -0.495em); top: -2.427em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-14329" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span><span style="position: absolute; clip: rect(1.45em, 1000em, 2.278em, -0.505em); top: -1.789em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14330" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14331" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14332" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14333" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14334" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14335" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14336" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14337" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14338" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14339" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14340" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14341" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14342" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14343" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.364em; left: 0em;"><span id="MathJax-Span-14344" class="mtd"><span id="MathJax-Span-14345" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14346" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14347" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14348" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14350" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14351" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14352" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14353" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14354" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14355" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14356" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.79em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.335em; vertical-align: -3.416em;"></span></span></nobr></span><script id="MathJax-Element-574" type="math/tex">\begin{array}[t]{l}
+\forall id,start,end,a_1,a_1',a_2,a_2',e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
+\\
+\qquad wasInformedBy(id,a_2,a_1,attrs) \wedge wasStartedBy(start,a_1,e_1,a_1',t_1,attrs_1) \wedge wasEndedBy(end,a_2,e_2,a_2',t_2,attrs_2)
+\\
+\quad\Rightarrow
+start \preceq end
+\end{array}</script></div>
+<div class="constraint" number="36" id="generation-precedes-invalidation"><div class="ruleTitle"><a href="#generation-precedes-invalidation" class="internalDFN">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-575-Frame" class="MathJax"><nobr><span id="MathJax-Span-14357" class="math"><span style="display: inline-block; position: relative; width: 585px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.075em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14358" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14359" class="mtable"><span style="display: inline-block; position: relative; width: 33.82em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.528em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.82em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14360" class="mtd"><span id="MathJax-Span-14361" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14362" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14363" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14364" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14365" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14366" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14367" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14368" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14369" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14370" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14371" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14372" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14373" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14374" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14375" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14376" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14378" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14379" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14380" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14381" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14382" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14383" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14384" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14385" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14386" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14387" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14388" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14389" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14390" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14392" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14393" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14394" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14395" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14396" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14397" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14398" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14400" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14401" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14402" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14403" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14404" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14405" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14406" class="mtd"><span id="MathJax-Span-14407" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14408" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14409" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14410" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14411" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14412" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14413" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14414" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14415" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14416" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14417" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14418" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14419" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14420" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14421" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14422" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14423" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14424" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14425" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14426" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14427" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14428" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14429" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14430" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14431" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14432" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14433" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14434" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14435" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14436" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14437" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14439" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14441" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14442" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14443" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14444" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14445" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14446" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14447" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14448" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14449" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14450" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14451" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14452" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14453" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14454" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14455" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14456" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14457" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14458" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14459" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14460" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14461" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14462" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14463" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14465" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14466" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14467" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14468" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14471" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14473" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14474" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14476" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14477" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14478" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14480" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14481" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14482" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14483" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14484" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14485" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.526em); top: 0.079em; left: 0em;"><span id="MathJax-Span-14486" class="mtd"><span id="MathJax-Span-14487" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14488" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14489" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14490" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14491" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14492" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14493" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14494" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14495" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14496" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.036em; vertical-align: -3.117em;"></span></span></nobr></span><script id="MathJax-Element-575" type="math/tex">\begin{array}[t]{l}
+\forall gen,inv,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen \preceq inv
+\end{array}</script></div>
+<div class="constraint" number="37" id="generation-precedes-usage"><div class="ruleTitle"><a href="#generation-precedes-usage" class="internalDFN">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-576-Frame" class="MathJax"><nobr><span id="MathJax-Span-14497" class="math"><span style="display: inline-block; position: relative; width: 495px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14498" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14499" class="mtable"><span style="display: inline-block; position: relative; width: 28.563em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.563em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14500" class="mtd"><span id="MathJax-Span-14501" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14502" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14503" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14504" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14505" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14506" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14507" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14508" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14509" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14510" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14511" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14512" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14513" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14514" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14515" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14516" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14517" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14518" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14519" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14520" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14521" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14522" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14523" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14524" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14525" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14526" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14527" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14528" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14529" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14530" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14532" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14533" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14534" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14535" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14536" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14537" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14538" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14540" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14541" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14542" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14543" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14544" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14545" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14546" class="mtd"><span id="MathJax-Span-14547" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14548" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14549" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14550" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14551" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14552" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14554" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14555" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14556" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14557" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14559" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14560" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14561" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14562" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14563" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14564" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14565" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14566" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14567" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14568" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14569" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14571" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14572" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14573" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14574" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14575" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14576" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14577" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14578" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14579" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14581" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14582" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14583" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14584" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14585" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14586" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14587" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14588" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14590" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14591" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14592" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14593" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14594" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14595" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14597" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14598" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14599" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14600" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14601" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14603" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14604" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14605" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14606" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14607" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14608" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14609" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14611" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14612" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14613" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14614" class="mtd"><span id="MathJax-Span-14615" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14616" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14617" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14618" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14620" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14621" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14622" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14623" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14624" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-576" type="math/tex">\begin{array}[t]{l}
+\forall gen,use,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge used(use,a_2,e,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen \preceq use
+\end{array}</script></div>
+<div class="constraint" number="38" id="usage-precedes-invalidation"><div class="ruleTitle"><a href="#usage-precedes-invalidation" class="internalDFN">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-577-Frame" class="MathJax"><nobr><span id="MathJax-Span-14625" class="math"><span style="display: inline-block; position: relative; width: 497px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14626" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14627" class="mtable"><span style="display: inline-block; position: relative; width: 28.68em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.252em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 28.68em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14628" class="mtd"><span id="MathJax-Span-14629" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14630" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14631" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14632" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14633" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14634" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14635" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14636" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14637" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14638" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14639" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14640" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14641" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14642" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14643" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14644" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14645" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14646" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14647" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14648" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14649" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14650" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14651" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14652" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14653" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14654" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14655" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14656" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14657" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14660" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14661" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14662" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14663" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14664" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14665" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14666" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14668" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14669" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14670" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14671" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14672" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14673" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-14674" class="mtd"><span id="MathJax-Span-14675" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14676" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14677" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14678" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14679" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14680" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14681" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14682" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14683" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14684" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14685" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14686" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14687" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14688" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14689" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14690" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14691" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14692" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14693" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14694" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14695" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14696" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14697" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14698" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14699" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14700" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14701" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14702" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14703" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14704" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14705" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14706" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14707" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14708" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14709" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14710" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14711" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14712" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14713" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14714" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14715" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14717" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14718" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14719" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14720" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14721" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14722" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14723" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14724" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14725" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14726" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14727" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14728" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14729" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14730" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14731" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14732" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14733" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14734" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14735" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14736" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14737" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14738" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14739" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14740" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14741" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14742" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14743" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-14744" class="mtd"><span id="MathJax-Span-14745" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14746" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14747" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14748" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14749" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14750" class="mi">e</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14751" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14752" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14753" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14754" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-577" type="math/tex">\begin{array}[t]{l}
+\forall use,inv,a_1,a_2,e,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad used(use,a_1,e,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+use \preceq inv
+\end{array}</script></div>
+<div class="constraint" number="39" id="generation-generation-ordering"><div class="ruleTitle"><a href="#generation-generation-ordering" class="internalDFN">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-578-Frame" class="MathJax"><nobr><span id="MathJax-Span-14755" class="math"><span style="display: inline-block; position: relative; width: 598px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14756" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14757" class="mtable"><span style="display: inline-block; position: relative; width: 34.579em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.579em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14758" class="mtd"><span id="MathJax-Span-14759" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14760" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14761" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14762" class="mi">e</span><span id="MathJax-Span-14763" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14764" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14765" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14766" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14767" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14768" class="mi">e</span><span id="MathJax-Span-14769" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14770" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14771" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14772" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14773" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14774" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14776" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14777" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14778" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14779" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14780" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14781" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14782" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14784" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14785" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14786" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14787" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14789" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14790" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14791" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14792" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14793" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14794" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14795" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14796" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14797" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14798" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14799" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14801" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14802" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14804" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14805" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14806" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14807" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-14808" class="mtd"><span id="MathJax-Span-14809" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14810" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14811" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14812" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14813" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14814" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14815" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14816" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14817" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14819" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14820" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14821" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14822" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14823" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14824" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14825" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14826" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14827" class="mi">e</span><span id="MathJax-Span-14828" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14829" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14830" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14831" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14832" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14833" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14834" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14835" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14836" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14837" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14838" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14839" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14840" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14841" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14842" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14844" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14845" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14846" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14847" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14848" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14849" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-14850" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-14851" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14852" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14853" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14854" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14855" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14856" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14857" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14858" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14859" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14861" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14862" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14863" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14864" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14865" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14866" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14867" class="mi">e</span><span id="MathJax-Span-14868" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14869" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14870" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14871" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14872" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14873" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14874" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14875" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14876" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14877" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14878" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14879" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14880" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14881" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14882" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14883" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14884" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14885" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14886" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14887" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14888" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14889" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-14890" class="mtd"><span id="MathJax-Span-14891" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-14892" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14893" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14894" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14895" class="mi">e</span><span id="MathJax-Span-14896" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14897" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14898" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-14899" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-14900" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14901" class="mi">e</span><span id="MathJax-Span-14902" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14903" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14904" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-578" type="math/tex">\begin{array}[t]{l}
+\forall gen_1,gen_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen_1,e,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \preceq gen_2
+\end{array}</script></div>
+<div class="constraint" number="40" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a href="#invalidation-invalidation-ordering" class="internalDFN">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-579-Frame" class="MathJax"><nobr><span id="MathJax-Span-14905" class="math"><span style="display: inline-block; position: relative; width: 604px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-14906" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-14907" class="mtable"><span style="display: inline-block; position: relative; width: 34.93em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.299em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 34.93em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-14908" class="mtd"><span id="MathJax-Span-14909" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-14910" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14911" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14912" class="mi">n</span><span id="MathJax-Span-14913" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14914" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14915" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14916" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14917" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14918" class="mi">n</span><span id="MathJax-Span-14919" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14920" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14921" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14922" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14923" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14924" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14925" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14926" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14927" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14928" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14929" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14930" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14931" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14932" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14933" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14934" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14935" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14936" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14937" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14939" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14940" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14941" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14942" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14943" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14944" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14946" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14948" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14949" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14950" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14951" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14952" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14953" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14954" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14955" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14956" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-14957" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-14958" class="mtd"><span id="MathJax-Span-14959" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-14960" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14961" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14962" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14963" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14965" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14966" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14967" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14968" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14969" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14970" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14971" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14972" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14973" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14974" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14975" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14976" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14977" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14978" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14979" class="mi">n</span><span id="MathJax-Span-14980" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14981" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14982" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14983" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14984" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-14985" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14986" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14987" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14988" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14989" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-14990" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14991" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-14992" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-14993" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-14994" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14996" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14997" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-14998" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-14999" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15000" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15001" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15002" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15003" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15004" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15005" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15006" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15007" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15008" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15009" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15010" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15011" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15012" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15013" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15014" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15015" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15016" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15017" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15018" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15019" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15020" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15021" class="mi">n</span><span id="MathJax-Span-15022" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15023" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15024" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15025" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15026" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15029" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15030" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15031" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15032" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15033" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15034" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15035" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15036" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15037" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15038" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15039" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15040" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15041" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15042" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15043" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-15044" class="mtd"><span id="MathJax-Span-15045" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15046" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15047" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15048" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15049" class="mi">n</span><span id="MathJax-Span-15050" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15051" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15052" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15053" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15054" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15055" class="mi">n</span><span id="MathJax-Span-15056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15057" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15058" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-579" type="math/tex">\begin{array}[t]{l}
+\forall inv_1,inv_2,e,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasInvalidatedBy(inv_1,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+inv_1 \preceq inv_2
+\end{array}</script></div>
+<div class="constraint" number="41" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a href="#derivation-usage-generation-ordering" class="internalDFN">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-580-Frame" class="MathJax"><nobr><span id="MathJax-Span-15059" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15060" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15061" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-580" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-581-Frame" class="MathJax"><nobr><span id="MathJax-Span-15062" class="math"><span style="display: inline-block; position: relative; width: 32px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15063" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15064" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15065" class="mi">e</span><span id="MathJax-Span-15066" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15067" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15068" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-581" type="math/tex">gen_2</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-582-Frame" class="MathJax"><nobr><span id="MathJax-Span-15069" class="math"><span style="display: inline-block; position: relative; width: 31px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.895em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15070" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15071" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15072" class="mi">s</span><span id="MathJax-Span-15073" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15074" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15075" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.758em; vertical-align: -0.223em;"></span></span></nobr></span><script id="MathJax-Element-582" type="math/tex">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-583-Frame" class="MathJax"><nobr><span id="MathJax-Span-15076" class="math"><span style="display: inline-block; position: relative; width: 686px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15077" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15078" class="mtable"><span style="display: inline-block; position: relative; width: 39.72em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 39.72em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15079" class="mtd"><span id="MathJax-Span-15080" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15081" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15082" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15083" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15084" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15085" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15086" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15087" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15088" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15089" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15090" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15091" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15092" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15093" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15094" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15095" class="mi">e</span><span id="MathJax-Span-15096" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15097" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15098" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15099" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15100" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15101" class="mi">s</span><span id="MathJax-Span-15102" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15103" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15104" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15105" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15108" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15109" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15110" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15111" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15112" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15113" class="mtd"><span id="MathJax-Span-15114" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15115" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15116" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15117" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15118" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15119" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15120" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15121" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15122" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15123" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15124" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15125" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15126" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15127" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15130" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15131" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15132" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15133" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15134" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15135" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15136" class="mi">e</span><span id="MathJax-Span-15137" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15138" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15139" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15140" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15141" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15142" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15143" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15144" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15145" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15146" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15147" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15148" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15149" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15150" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15151" class="mi">s</span><span id="MathJax-Span-15152" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15153" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15154" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15155" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15156" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15157" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15158" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15159" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15160" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15161" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15162" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15163" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15164" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15165" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15166" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15167" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15168" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15169" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15170" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15171" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15172" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15173" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15174" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15175" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15176" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15177" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15178" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15179" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15180" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15181" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15182" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15183" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15184" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15185" class="mi">e</span><span id="MathJax-Span-15186" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15187" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15188" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15189" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15190" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15191" class="mi">s</span><span id="MathJax-Span-15192" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15193" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15194" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15195" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15196" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15197" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15198" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15199" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15200" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15201" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-15202" class="mtd"><span id="MathJax-Span-15203" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15204" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15205" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15206" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15207" class="mi">s</span><span id="MathJax-Span-15208" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15209" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15210" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15211" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15212" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15213" class="mi">e</span><span id="MathJax-Span-15214" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15215" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15216" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-583" type="math/tex">\begin{array}[t]{l}
+\forall d,e_1,e_2,a,gen_2,use_1,attrs.~
+\\
+\qquad notNull(a) \wedge notNull(gen_2) \wedge notNull(use_1) \wedge wasDerivedFrom(d,e_2,e_1,a,gen_2,use_1,attrs)
+\\
+\quad\Rightarrow
+use_1 \preceq gen_2
+\end{array}</script></div>
+<div class="constraint" number="42" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a href="#derivation-generation-generation-ordering" class="internalDFN">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-584-Frame" class="MathJax"><nobr><span id="MathJax-Span-15217" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15218" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15219" class="mi">a</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-584" type="math/tex">a</script>,<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-585-Frame" class="MathJax"><nobr><span id="MathJax-Span-15220" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15221" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15222" class="mi">g</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-585" type="math/tex">g</script>, or <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-586-Frame" class="MathJax"><nobr><span id="MathJax-Span-15223" class="math"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15224" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15225" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.609em; vertical-align: -0.074em;"></span></span></nobr></span><script id="MathJax-Element-586" type="math/tex">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-587-Frame" class="MathJax"><nobr><span id="MathJax-Span-15226" class="math"><span style="display: inline-block; position: relative; width: 908px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.972em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15227" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15228" class="mtable"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(3.581em, 1000em, 7.366em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15229" class="mtd"><span id="MathJax-Span-15230" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15231" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15232" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15233" class="mo">,</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-15348" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15349" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15350" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15351" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15352" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15353" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15354" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15355" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15356" class="mi">e</span><span id="MathJax-Span-15357" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15358" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15359" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15362" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15364" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15365" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15366" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15367" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15368" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15369" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15371" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15374" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15378" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15379" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15380" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15381" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15382" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15383" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15384" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15385" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15387" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15389" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15391" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15392" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15393" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15394" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15395" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15396" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15397" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15398" class="mi">e</span><span id="MathJax-Span-15399" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15400" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15401" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15402" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15403" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15404" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15405" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15406" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15407" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15408" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15409" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15410" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15411" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15413" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15414" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15415" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15416" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15417" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15418" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15419" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15420" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15421" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15422" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.844em, 1000em, 2.951em, -0.526em); top: -0.024em; left: 0em;"><span id="MathJax-Span-15423" class="mtd"><span id="MathJax-Span-15424" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15425" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15426" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15427" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15428" class="mi">e</span><span id="MathJax-Span-15429" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15430" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15431" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15432" class="mo">≺</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15433" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15434" class="mi">e</span><span id="MathJax-Span-15435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15436" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15437" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.926em; vertical-align: -3.007em;"></span></span></nobr></span><script id="MathJax-Element-587" type="math/tex">\begin{array}[t]{l}
+\forall d,gen_1,gen_2,e_1,e_2,a,a_1,a_2,g,u,t_1,t_2,attrs,attrs_1,attrs_2.~
+\\
+\qquad wasDerivedFrom(d,e_2,e_1,a,g,u,attrs) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \prec gen_2
+\end{array}</script></div>
+<div class="constraint" number="43" id="wasStartedBy-ordering"><div class="ruleTitle"><a href="#wasStartedBy-ordering" class="internalDFN">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-588-Frame" class="MathJax"><nobr><span id="MathJax-Span-15438" class="math"><span style="display: inline-block; position: relative; width: 584px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15439" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15440" class="mtable"><span style="display: inline-block; position: relative; width: 33.762em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.762em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15441" class="mtd"><span id="MathJax-Span-15442" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15443" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15444" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15445" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15446" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15447" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15448" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15449" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15450" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15451" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15452" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15453" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15454" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15456" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15459" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15463" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15464" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15468" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15469" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15470" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15472" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15473" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15475" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15476" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15477" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15478" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15479" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15480" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15481" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15484" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15485" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15486" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15487" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15488" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15489" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15490" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15491" class="mtd"><span id="MathJax-Span-15492" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15493" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15494" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15495" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15496" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15497" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15498" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15499" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15500" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15501" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15502" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15503" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15504" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15505" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15506" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15507" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15508" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15509" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15510" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15511" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15512" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15513" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15514" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15515" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15516" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15517" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15518" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15519" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15520" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15521" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15522" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15523" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15526" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15527" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15528" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15529" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15530" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15531" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15532" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15533" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15534" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15535" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15537" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15539" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15540" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15541" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15542" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15543" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15544" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15545" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15547" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15548" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15549" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15550" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15551" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15552" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15553" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15554" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15555" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15556" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15557" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15558" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15559" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15560" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15561" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15562" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15563" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15564" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15565" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15566" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15568" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15569" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15570" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-15571" class="mtd"><span id="MathJax-Span-15572" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15573" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15574" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15575" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15576" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15577" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15578" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15579" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15580" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15581" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15582" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15583" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-588" type="math/tex">\begin{array}[t]{l}
+\forall gen,start,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasStartedBy(start,a,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen \preceq start
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-589-Frame" class="MathJax"><nobr><span id="MathJax-Span-15584" class="math"><span style="display: inline-block; position: relative; width: 587px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15585" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15586" class="mtable"><span style="display: inline-block; position: relative; width: 33.937em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.252em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.937em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15587" class="mtd"><span id="MathJax-Span-15588" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15589" class="mi">∀</span><span style="font-family: STIXGeneral; 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width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15710" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15711" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15712" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15713" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15714" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15715" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15716" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15717" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15718" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.848em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-15719" class="mtd"><span id="MathJax-Span-15720" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15721" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15722" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15723" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15725" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15726" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15727" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15728" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15729" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15730" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15731" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-589" type="math/tex">\begin{array}[t]{l}
+\forall start,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasStartedBy(start,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start \preceq inv
+\end{array}</script></li></ol></div>
+<div class="constraint" number="44" id="wasEndedBy-ordering"><div class="ruleTitle"><a href="#wasEndedBy-ordering" class="internalDFN">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-590-Frame" class="MathJax"><nobr><span id="MathJax-Span-15732" class="math"><span style="display: inline-block; position: relative; width: 571px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15733" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15734" class="mtable"><span style="display: inline-block; position: relative; width: 33.002em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.002em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15735" class="mtd"><span id="MathJax-Span-15736" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15737" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15738" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15739" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15740" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15741" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15742" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15743" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15744" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15745" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15746" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15747" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15748" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15749" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15750" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15751" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15752" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15753" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15754" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15755" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15756" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15757" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15758" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15759" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15760" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15761" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15762" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15763" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15764" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15765" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15766" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15767" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15769" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15770" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15771" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15772" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15773" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15774" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15775" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15776" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15777" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15778" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15779" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15780" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15781" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15782" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-15783" class="mtd"><span id="MathJax-Span-15784" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15785" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15786" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15787" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15788" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15789" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15790" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15791" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15792" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15793" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15794" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15796" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15797" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15798" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15799" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15800" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15801" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15802" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15803" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15804" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15805" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15806" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15808" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15809" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15810" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15811" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15812" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15813" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15814" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15815" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15816" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15817" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15818" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15819" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15820" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15821" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15822" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15823" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15824" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15825" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15826" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15827" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15828" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15829" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15830" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15831" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15832" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15833" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15834" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15835" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15836" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15837" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15838" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15839" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15840" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15841" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15842" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15843" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15844" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15845" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15846" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15847" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15848" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15849" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15850" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15851" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15852" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15853" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15854" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15856" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15857" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15858" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-15859" class="mtd"><span id="MathJax-Span-15860" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-15861" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15862" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15863" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15865" class="mi">n</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-15866" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-15867" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15868" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15869" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-590" type="math/tex">\begin{array}[t]{l}
+\forall gen,end,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasGeneratedBy(gen,e,a_1,t_1,attrs_1) \wedge wasEndedBy(end,a,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen \preceq end
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-591-Frame" class="MathJax"><nobr><span id="MathJax-Span-15870" class="math"><span style="display: inline-block; position: relative; width: 573px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.042em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-15871" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-15872" class="mtable"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.281em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 33.119em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-15873" class="mtd"><span id="MathJax-Span-15874" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-15875" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15876" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15877" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15878" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15879" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15880" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15881" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15882" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15883" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15884" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15886" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15887" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15888" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15889" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15890" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15891" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15892" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15893" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15894" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15895" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15896" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15897" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15898" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15899" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15900" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15901" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15902" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15903" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15904" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15905" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15906" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15907" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15908" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15909" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15910" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15911" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15912" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15913" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15914" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15915" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15916" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15917" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15918" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15919" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-15920" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-15921" class="mtd"><span id="MathJax-Span-15922" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-15923" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15924" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15925" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15926" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15927" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15928" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15929" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15930" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15931" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15932" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15933" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15934" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15935" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15936" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15937" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15938" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15939" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15940" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15941" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15942" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15943" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15944" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15945" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15946" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15947" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15949" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15950" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15951" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15952" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15953" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15954" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15955" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15956" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15957" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15958" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-15959" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-15960" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15961" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15962" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15963" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15964" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15965" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15966" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15967" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15968" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15969" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15970" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15971" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15977" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15978" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15979" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15980" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15981" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-15982" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15983" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15984" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15985" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15986" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-15987" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15988" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15989" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15990" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-15991" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15992" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15993" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15994" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-15995" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15996" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-15997" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-15998" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.848em, -0.526em); top: 0.052em; left: 0em;"><span id="MathJax-Span-15999" class="mtd"><span id="MathJax-Span-16000" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16001" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16002" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16003" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16004" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16005" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16006" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16007" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16008" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16009" class="mi">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.001em; vertical-align: -3.082em;"></span></span></nobr></span><script id="MathJax-Element-591" type="math/tex">\begin{array}[t]{l}
+\forall end,inv,e,a,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasEndedBy(end,a,e,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+end \preceq inv
+\end{array}</script></li></ol></div>
+<div class="constraint" number="45" id="specialization-generation-ordering"><div class="ruleTitle"><a href="#specialization-generation-ordering" class="internalDFN">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-592-Frame" class="MathJax"><nobr><span id="MathJax-Span-16010" class="math"><span style="display: inline-block; position: relative; width: 797px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.031em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16011" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16012" class="mtable"><span style="display: inline-block; position: relative; width: 46.203em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.484em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 46.203em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16013" class="mtd"><span id="MathJax-Span-16014" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16015" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16016" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16017" class="mi">e</span><span id="MathJax-Span-16018" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16019" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16020" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16021" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16022" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16023" class="mi">e</span><span id="MathJax-Span-16024" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16025" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16026" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16027" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16028" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16029" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16030" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16031" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16032" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16033" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16034" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16035" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16036" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16037" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16038" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16039" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16040" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16041" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16042" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16043" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16044" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16045" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16046" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16047" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16048" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16049" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16050" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16051" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16052" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16053" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16054" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16055" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16057" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16058" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16059" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16060" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16062" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16063" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16064" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16065" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16066" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16067" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-16068" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-16069" class="mtd"><span id="MathJax-Span-16070" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-16071" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16072" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16073" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16074" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16075" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16076" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16078" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16079" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16080" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16081" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16082" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16084" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16085" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16086" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16087" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16088" class="mo">(</span><span id="MathJax-Span-16089" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16090" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16091" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16092" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16093" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16094" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16095" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16096" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16097" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16098" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16099" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16100" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16101" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16102" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16103" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16104" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16105" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16106" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16107" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16108" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16109" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16110" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16111" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16112" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16113" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16114" class="mi">e</span><span id="MathJax-Span-16115" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16116" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16117" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16118" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16119" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16120" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16121" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16122" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16123" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16124" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16125" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16126" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16127" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16128" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16129" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16130" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16131" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16132" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16133" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16134" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16135" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16136" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16137" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16138" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16139" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16140" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16141" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16142" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16143" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16144" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16145" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16146" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16147" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16148" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16149" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16150" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16151" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16152" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16153" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16154" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16155" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16156" class="mi">e</span><span id="MathJax-Span-16157" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16158" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16159" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16160" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16161" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16162" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16163" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16164" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16165" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16166" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16167" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16168" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16169" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16171" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16172" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16173" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16174" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16175" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16176" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16177" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16178" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16179" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16180" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.035em; left: 0em;"><span id="MathJax-Span-16181" class="mtd"><span id="MathJax-Span-16182" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16183" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16184" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16185" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16186" class="mi">e</span><span id="MathJax-Span-16187" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16188" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16189" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16190" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16191" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16192" class="mi">e</span><span id="MathJax-Span-16193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16194" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16195" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.989em; vertical-align: -3.07em;"></span></span></nobr></span><script id="MathJax-Element-592" type="math/tex">\begin{array}[t]{l}
+\forall gen_1,gen_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad specializationOf(e_2,e_1) \wedge wasGeneratedBy(gen_1,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \preceq gen_2
+\end{array}</script></div>
+<div class="constraint" number="46" id="specialization-invalidation-ordering"><div class="ruleTitle"><a href="#specialization-invalidation-ordering" class="internalDFN">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-593-Frame" class="MathJax"><nobr><span id="MathJax-Span-16196" class="math"><span style="display: inline-block; position: relative; width: 803px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.014em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16197" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16198" class="mtable"><span style="display: inline-block; position: relative; width: 46.554em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.3em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 46.554em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16199" class="mtd"><span id="MathJax-Span-16200" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16201" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16202" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16203" class="mi">n</span><span id="MathJax-Span-16204" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16205" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16206" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16207" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16208" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16209" class="mi">n</span><span id="MathJax-Span-16210" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16211" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16212" class="mn">2</span><span style="display: inline-block; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16325" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16326" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16327" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16328" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16329" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16331" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16332" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16333" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16335" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16336" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16338" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16339" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16340" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16341" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16342" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16343" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16344" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16345" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16346" class="mi">n</span><span id="MathJax-Span-16347" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16348" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16349" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16350" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16351" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16352" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16353" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16354" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16355" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16356" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16357" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16358" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16359" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16360" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16361" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16362" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16366" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16367" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16368" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16369" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16370" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.024em; left: 0em;"><span id="MathJax-Span-16371" class="mtd"><span id="MathJax-Span-16372" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16373" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16374" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16375" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16376" class="mi">n</span><span id="MathJax-Span-16377" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16378" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16379" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16380" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16381" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16382" class="mi">n</span><span id="MathJax-Span-16383" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16384" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16385" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.971em; vertical-align: -3.052em;"></span></span></nobr></span><script id="MathJax-Element-593" type="math/tex">\begin{array}[t]{l}
+\forall inv_1,inv_2,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad specializationOf(e_1,e_2) \wedge wasInvalidatedBy(inv_1,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+inv_1 \preceq inv_2
+\end{array}</script></div>
+<div class="constraint" number="47" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a href="#wasAssociatedWith-ordering" class="internalDFN">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-594-Frame" class="MathJax"><nobr><span id="MathJax-Span-16386" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.95em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16387" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16388" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16389" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.075em; vertical-align: -0.282em;"></span></span></nobr></span><script id="MathJax-Element-594" type="math/tex">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-595-Frame" class="MathJax"><nobr><span id="MathJax-Span-16390" class="math"><span style="display: inline-block; position: relative; width: 925px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.069em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16391" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16392" class="mtable"><span style="display: inline-block; position: relative; width: 53.68em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.413em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.68em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16393" class="mtd"><span id="MathJax-Span-16394" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16395" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16396" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16397" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16398" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16399" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16400" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16401" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16402" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16403" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16404" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16405" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16406" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16407" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16408" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16409" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16410" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16411" class="mi">n</span><span id="MathJax-Span-16412" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16413" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16414" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16415" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16416" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16417" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16418" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16419" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16420" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16421" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16422" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16423" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16424" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16425" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16426" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16427" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16428" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16429" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16430" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16431" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16432" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16433" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16434" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16435" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16436" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16437" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16438" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16439" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16441" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16442" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16443" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16444" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16445" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16446" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16447" class="msubsup"><span style="display: inline-block; 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padding-left: 0.25em;" id="MathJax-Span-16502" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16503" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16504" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16505" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16506" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16507" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16508" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16509" class="mi">t<span style="display: inline-block; 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font-style: italic;" id="MathJax-Span-16570" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16571" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16572" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16573" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16574" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16575" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16576" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16578" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16579" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16580" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16581" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16582" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16583" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16584" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16585" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16586" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16587" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.895em, -0.526em); top: 0.079em; left: 0em;"><span id="MathJax-Span-16588" class="mtd"><span id="MathJax-Span-16589" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16590" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16591" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16592" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16594" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16595" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16596" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16597" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16598" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16599" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16600" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16601" class="mi">n</span><span id="MathJax-Span-16602" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16603" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16604" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.029em; vertical-align: -3.111em;"></span></span></nobr></span><script id="MathJax-Element-595" type="math/tex">\begin{array}[t]{l}
+\forall assoc,start_1,inv_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq inv_2
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-596-Frame" class="MathJax"><nobr><span id="MathJax-Span-16605" class="math"><span style="display: inline-block; position: relative; width: 908px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.104em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16606" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16607" class="mtable"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.615em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 52.687em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16608" class="mtd"><span id="MathJax-Span-16609" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16610" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16611" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16612" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16613" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16614" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16615" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16616" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16617" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16618" class="mi">e</span><span id="MathJax-Span-16619" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16620" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16621" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16622" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16623" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16624" class="mi">n</span><span id="MathJax-Span-16625" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16626" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16627" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16628" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16630" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16631" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16632" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16633" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16634" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16635" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16636" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16637" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16638" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16639" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16640" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16641" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16642" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16643" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16644" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16645" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16646" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16647" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16648" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16650" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16651" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16653" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16654" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16656" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16657" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16658" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16659" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16660" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16661" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16662" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16663" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16664" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16665" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16666" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16667" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16668" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16669" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16670" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16671" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-16672" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-16673" class="mtd"><span id="MathJax-Span-16674" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-16675" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16676" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16677" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16678" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16679" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16680" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16681" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16682" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16683" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16684" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16685" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16686" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16687" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16688" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16689" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16690" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16691" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16692" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16693" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16694" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16695" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16696" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16697" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16698" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16699" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16700" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16701" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16702" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16703" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16704" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16705" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16706" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16707" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16708" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16709" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16710" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16711" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16712" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16713" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16714" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16715" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16716" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16717" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16718" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16719" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16720" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16721" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16722" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16723" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16724" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16725" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16726" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16727" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16728" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16729" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16730" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16731" class="mi">e</span><span id="MathJax-Span-16732" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16733" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16734" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16735" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16736" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16737" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16738" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16739" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16740" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16741" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16742" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16743" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16745" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16746" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16747" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16748" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16750" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16751" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16752" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16753" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16754" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16755" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16756" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16757" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16758" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16759" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16760" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16761" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16762" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16763" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16764" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16765" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16766" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16767" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16768" class="mi">n</span><span id="MathJax-Span-16769" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16770" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16771" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16772" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16773" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16774" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16776" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16777" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16778" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16779" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16780" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16781" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16782" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16783" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16784" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16785" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16786" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16787" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16788" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16789" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16790" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16791" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16792" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16793" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16794" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-16795" class="mtd"><span id="MathJax-Span-16796" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-16797" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16798" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16799" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16800" class="mi">e</span><span id="MathJax-Span-16801" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16802" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16803" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-16804" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-16805" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16806" class="mi">n</span><span id="MathJax-Span-16807" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16808" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16809" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.067em; vertical-align: -3.148em;"></span></span></nobr></span><script id="MathJax-Element-596" type="math/tex">\begin{array}[t]{l}
+\forall assoc,gen_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \preceq end_2
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-597-Frame" class="MathJax"><nobr><span id="MathJax-Span-16810" class="math"><span style="display: inline-block; position: relative; width: 916px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-16811" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-16812" class="mtable"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-16813" class="mtd"><span id="MathJax-Span-16814" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-16815" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16816" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16817" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16818" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16819" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16820" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16821" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16822" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16823" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16824" class="mi">a</span><span style="font-family: STIXGeneral; 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font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16836" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16837" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16838" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16839" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16840" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16841" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16842" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16843" class="msubsup"><span style="display: inline-block; 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width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16854" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16855" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16856" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16857" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16858" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16859" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16860" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16861" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16862" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16863" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16864" class="mi">t<span style="display: inline-block; 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vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-16882" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16883" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16884" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16885" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16886" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16887" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16888" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16889" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16890" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16891" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16892" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16894" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16895" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16896" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16897" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16898" class="mi">t<span style="display: inline-block; overflow: hidden; 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overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16932" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16933" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16934" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16935" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16936" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16937" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16938" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16939" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16940" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16941" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16942" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16943" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16944" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16945" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16946" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16947" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16948" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16949" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16950" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16951" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16952" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16953" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16954" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16955" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16956" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16957" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16958" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16959" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16960" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-16961" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16962" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16963" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16964" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-16965" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-16966" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16967" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16968" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16969" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16970" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16971" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16972" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16973" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16974" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16975" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16976" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16977" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16978" class="mi">n</span><span id="MathJax-Span-16979" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16980" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16981" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16982" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16983" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16984" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-16985" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16986" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16987" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16988" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16989" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16990" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16991" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16992" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16993" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-16994" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16995" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-16996" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-16997" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-16998" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16999" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17000" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17001" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17002" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17003" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17004" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17005" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-17006" class="mtd"><span id="MathJax-Span-17007" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17008" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17009" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17010" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17011" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17012" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17013" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17014" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17015" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17016" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17017" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17018" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17019" class="mi">n</span><span id="MathJax-Span-17020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17021" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17022" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-597" type="math/tex">\begin{array}[t]{l}
+\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,a,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq end_2
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-598-Frame" class="MathJax"><nobr><span id="MathJax-Span-17023" class="math"><span style="display: inline-block; position: relative; width: 916px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17024" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17025" class="mtable"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.501em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 53.154em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17026" class="mtd"><span id="MathJax-Span-17027" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17028" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17029" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17030" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17032" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17033" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17034" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17035" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17036" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17037" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17038" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17039" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17040" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17041" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17042" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17043" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17044" class="mi">n</span><span id="MathJax-Span-17045" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17046" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17047" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17048" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17049" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17050" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17051" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17052" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17053" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17054" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17055" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17056" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17057" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17058" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17059" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17060" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17061" class="mi">a</span><span style="display: inline-block; 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position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17176" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17177" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17178" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17179" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17180" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17181" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17182" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17183" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17184" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17185" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17186" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17187" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17188" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17189" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17190" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17192" class="mi">n</span><span id="MathJax-Span-17193" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17194" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17195" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17196" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17197" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17198" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17199" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17200" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17201" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17202" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17203" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17204" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17205" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17206" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17209" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17211" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17214" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17215" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17216" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17217" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17218" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-17219" class="mtd"><span id="MathJax-Span-17220" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17221" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17222" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17223" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17224" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17225" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17226" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17227" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17228" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17229" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17230" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17231" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17232" class="mi">n</span><span id="MathJax-Span-17233" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17234" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17235" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-598" type="math/tex">\begin{array}[t]{l}
+\forall assoc,start_1,end_2,ag,e_1,e_2,a_1,a_2,t_1,t_2,attrs_1,attrs_2.~
+\\
+\qquad wasAssociatedWith(assoc,a,ag,pl,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,a,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq end_2
+\end{array}</script></li></ol></div>
+<div class="constraint" number="48" id="wasAttributedTo-ordering"><div class="ruleTitle"><a href="#wasAttributedTo-ordering" class="internalDFN">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-599-Frame" class="MathJax"><nobr><span id="MathJax-Span-17236" class="math"><span style="display: inline-block; position: relative; width: 853px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17237" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17238" class="mtable"><span style="display: inline-block; position: relative; width: 49.474em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.474em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17239" class="mtd"><span id="MathJax-Span-17240" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17241" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17242" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17243" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17245" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17246" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17247" class="mi">e</span><span id="MathJax-Span-17248" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17249" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17250" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17251" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17252" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17253" class="mi">e</span><span id="MathJax-Span-17254" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17255" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17256" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17257" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17258" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17259" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17260" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17261" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17262" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17263" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17264" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17265" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17266" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17267" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17268" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17269" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17270" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17271" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17272" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17273" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17274" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17276" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17277" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17278" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17279" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17280" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17281" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17282" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17283" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17284" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17285" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17286" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17287" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17288" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17289" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17290" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17291" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17292" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17293" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17294" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17295" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17296" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17297" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17298" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17299" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17300" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-17301" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-17302" class="mtd"><span id="MathJax-Span-17303" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-17304" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17305" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17306" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17307" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17308" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17309" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17310" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17311" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17312" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17313" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17314" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17316" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17317" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17318" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17319" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17321" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17322" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17323" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17324" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17325" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17326" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17327" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17328" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17329" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17330" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17331" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17332" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17333" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17334" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17335" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17336" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17337" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17338" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17339" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17340" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17341" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17342" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17343" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17344" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17345" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17346" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17347" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17348" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17349" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17350" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17351" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17352" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17353" class="mi">e</span><span id="MathJax-Span-17354" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17355" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17356" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17357" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17358" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17359" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17360" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17361" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17362" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17363" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17364" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17365" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17367" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17368" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17369" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17370" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17371" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17372" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17373" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17374" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17375" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17376" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17377" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17378" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17379" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17380" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17381" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17382" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17383" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17385" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17386" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17387" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17388" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17389" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17390" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17391" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17392" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17393" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17394" class="mi">e</span><span id="MathJax-Span-17395" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17396" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17397" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17398" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17399" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17400" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17401" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17402" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17403" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17404" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17405" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17406" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17407" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17408" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17409" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17410" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17411" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17412" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17413" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17414" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17415" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17416" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-17417" class="mtd"><span id="MathJax-Span-17418" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17419" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17420" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17421" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17422" class="mi">e</span><span id="MathJax-Span-17423" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17424" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17425" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17426" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17427" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17428" class="mi">e</span><span id="MathJax-Span-17429" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17430" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17431" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-599" type="math/tex">\begin{array}[t]{l}
+\forall att,gen_1,gen_2,e,a_1,a_2,t_1,t_2,ag,attrs,attrs_1,attrs_2.~
+\\
+\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasGeneratedBy(gen_1,ag,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \preceq gen_2
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-600-Frame" class="MathJax"><nobr><span id="MathJax-Span-17432" class="math"><span style="display: inline-block; position: relative; width: 861px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.03em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17433" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17434" class="mtable"><span style="display: inline-block; position: relative; width: 49.942em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.483em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 49.942em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17435" class="mtd"><span id="MathJax-Span-17436" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17437" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17438" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17439" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17440" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17441" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17442" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17443" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17444" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17445" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17446" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17447" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17448" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17449" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17450" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17451" class="mi">e</span><span id="MathJax-Span-17452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17453" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17455" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17456" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17457" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17458" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17459" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17460" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17461" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17462" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17463" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17464" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17465" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17466" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17467" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17468" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17469" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17470" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17471" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17472" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17473" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17474" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17475" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17476" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17477" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17478" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17479" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17480" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17481" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17482" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17484" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17485" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17486" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17487" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17489" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17490" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17491" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17492" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17493" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17494" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17495" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17496" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17497" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17498" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17499" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17500" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17501" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17502" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-17503" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-17504" class="mtd"><span id="MathJax-Span-17505" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-17506" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17507" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17509" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17510" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17511" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17512" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17513" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17514" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17515" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17516" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17517" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17518" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17519" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17520" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17521" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17522" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17523" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17524" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17525" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17526" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17527" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17528" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17529" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17530" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17531" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17532" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17533" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17534" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17535" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17536" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17537" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17538" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17539" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17540" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17541" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17542" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17543" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17544" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17545" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17546" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17547" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17548" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17549" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17550" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17551" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17552" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17553" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17554" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17555" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17556" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17557" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17558" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17559" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17560" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17561" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17562" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17564" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17565" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17566" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17568" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17569" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17570" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17571" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17572" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17573" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17574" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17575" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17578" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17579" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17580" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17581" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17582" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17583" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17584" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17585" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17586" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17587" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17588" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17589" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17590" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17591" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17592" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17594" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17595" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17596" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17597" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17598" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17600" class="mi">e</span><span id="MathJax-Span-17601" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17602" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17603" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17604" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17605" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17606" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17607" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17608" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17609" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17610" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17611" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17612" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17613" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17614" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17615" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17616" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17618" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17619" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17620" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17621" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17622" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.786em, 1000em, 2.951em, -0.526em); top: 0.034em; left: 0em;"><span id="MathJax-Span-17623" class="mtd"><span id="MathJax-Span-17624" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17625" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17626" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17627" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17628" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17629" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17631" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17633" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17634" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17635" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17636" class="mi">e</span><span id="MathJax-Span-17637" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17638" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17639" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.988em; vertical-align: -3.069em;"></span></span></nobr></span><script id="MathJax-Element-600" type="math/tex">\begin{array}[t]{l}
+\forall att,start_1,gen_2,e,e_1,a_1,a_2,ag,t_1,t_2,attrs,attrs_1,attrs_2.~
+\\
+\qquad wasAttributedTo(att,e,ag,attrs) \wedge wasStartedBy(start_1,ag,e_1,a_1,t_1,attrs_1) \wedge wasGeneratedBy(gen_2,e,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq gen_2
+\end{array}</script></li></ol></div>
+<div class="constraint" number="49" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a href="#actedOnBehalfOf-ordering" class="internalDFN">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-601-Frame" class="MathJax"><nobr><span id="MathJax-Span-17640" class="math"><span style="display: inline-block; position: relative; width: 934px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.145em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17641" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17642" class="mtable"><span style="display: inline-block; position: relative; width: 54.206em; height: 0px;"><span style="position: absolute; clip: rect(3.756em, 1000em, 7.715em, -0.526em); top: -4.614em; left: 0em;"><span style="display: inline-block; position: relative; width: 54.206em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17643" class="mtd"><span id="MathJax-Span-17644" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17645" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17646" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17647" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17648" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17649" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17650" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17651" class="mi">e</span><span id="MathJax-Span-17652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17653" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17654" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17655" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17656" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17657" class="mi">n</span><span id="MathJax-Span-17658" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17659" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17660" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17661" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17662" class="mi">a</span><span id="MathJax-Span-17663" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17664" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17665" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17666" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17667" class="mi">a</span><span id="MathJax-Span-17668" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17669" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17670" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17671" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17672" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17673" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17674" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17675" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17676" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17677" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17678" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17679" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17680" class="mn">2</span><span style="display: inline-block; 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position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17794" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17795" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17796" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-17797" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-17798" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17799" class="mi">a</span><span style="font-family: STIXGeneral; 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height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17808" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17809" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17810" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17811" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17812" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17813" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17814" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17815" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17816" class="mi">n</span><span id="MathJax-Span-17817" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17818" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17819" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17820" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17821" class="mi">a</span><span id="MathJax-Span-17822" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17823" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17824" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17825" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17826" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17827" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17828" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17829" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17830" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17831" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17832" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17833" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17834" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17835" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17836" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17837" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17838" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17839" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17840" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17841" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.741em, 1000em, 2.951em, -0.526em); top: 0.15em; left: 0em;"><span id="MathJax-Span-17842" class="mtd"><span id="MathJax-Span-17843" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-17844" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17845" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17846" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17847" class="mi">e</span><span id="MathJax-Span-17848" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.754em, -0.512em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17849" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17850" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17851" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-17852" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17853" class="mi">n</span><span id="MathJax-Span-17854" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.763em, -0.506em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17855" class="mi">v</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17856" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.614em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.112em; vertical-align: -3.193em;"></span></span></nobr></span><script id="MathJax-Element-601" type="math/tex">\begin{array}[t]{l}
+\forall del,gen_1,inv_2,ag_1,ag_2,a,a_1,a_2,t_1,t_2,attrs,attrs_1,attrs_2.~
+\\
+\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasGeneratedBy(gen_1,ag_1,a_1,t_1,attrs_1) \wedge wasInvalidatedBy(inv_2,ag_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+gen_1 \preceq inv_2
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-602-Frame" class="MathJax"><nobr><span id="MathJax-Span-17857" class="math"><span style="display: inline-block; position: relative; width: 933px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.168em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-17858" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-17859" class="mtable"><span style="display: inline-block; position: relative; width: 54.147em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.63em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 54.147em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-17860" class="mtd"><span id="MathJax-Span-17861" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-17862" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17863" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17864" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17865" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17866" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17867" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17868" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17869" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17870" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-17871" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17872" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17873" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17874" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17875" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17876" class="mi">n</span><span id="MathJax-Span-17877" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17878" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17879" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17880" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17881" class="mi">a</span><span id="MathJax-Span-17882" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17883" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17884" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17885" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17886" class="mi">a</span><span id="MathJax-Span-17887" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17888" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17889" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17890" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-17891" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-17892" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17893" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17894" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17895" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17896" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17897" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17898" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17899" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17900" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17901" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17902" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17903" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17904" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17905" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17906" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-17907" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-17908" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-17909" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-17910" class="mi">t<span style="display: inline-block; 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width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18026" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18027" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18028" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18029" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18031" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18032" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18033" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18034" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18035" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18036" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18037" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18038" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18039" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18040" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18041" class="mi">n</span><span id="MathJax-Span-18042" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18043" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18044" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18045" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18046" class="mi">a</span><span id="MathJax-Span-18047" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18048" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18049" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18050" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18051" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18052" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18053" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18054" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18056" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18057" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18058" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18059" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18060" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18061" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18062" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18063" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18064" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18065" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18066" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-18067" class="msubsup"><span style="display: inline-block; position: relative; width: 0.834em; height: 0px;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18068" class="mi">s</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.409em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18069" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18070" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.526em); top: 0.179em; left: 0em;"><span id="MathJax-Span-18071" class="mtd"><span id="MathJax-Span-18072" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18073" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18074" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18075" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18076" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18077" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18078" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span id="MathJax-Span-18079" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18080" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18081" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-18082" class="mo">⪯</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18083" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18084" class="mi">n</span><span id="MathJax-Span-18085" class="msubsup"><span style="display: inline-block; position: relative; width: 0.924em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.511em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18086" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.499em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18087" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.136em; vertical-align: -3.218em;"></span></span></nobr></span><script id="MathJax-Element-602" type="math/tex">\begin{array}[t]{l}
+\forall del,start_1,end_2,ag_1,ag_2,a,a_1,a_2,e_1,e_2,t_1,t_2,attrs,attrs_1,attrs_2.~
+\\
+\qquad actedOnBehalfOf(del,ag_2,ag_1,a,attrs) \wedge wasStartedBy(start_1,ag_1,e_1,a_1,t_1,attrs_1) \wedge wasEndedBy(end_2,ag_2,e_2,a_2,t_2,attrs_2)
+\\
+\quad\Rightarrow
+start_1 \preceq end_2
+\end{array}</script></li></ol></div>
+
+</section>
+
+<section id="typing-constraints">
+<h4><span class="secno">5.2.3 </span>Typing constraints</h4>
+
+<div class="constraint" number="50" id="typing"><div class="ruleTitle"><a href="#typing" class="internalDFN">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-603-Frame" class="MathJax"><nobr><span id="MathJax-Span-18088" class="math"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.028em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18089" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18090" class="mtable"><span style="display: inline-block; position: relative; width: 8.995em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.481em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 8.995em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18091" class="mtd"><span id="MathJax-Span-18092" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18093" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18094" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18095" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18096" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18097" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18098" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18099" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18100" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18101" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18102" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.303em; left: 0em;"><span id="MathJax-Span-18103" class="mtd"><span id="MathJax-Span-18104" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18105" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18106" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18107" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18108" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18109" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18110" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18111" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18112" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18113" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18114" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18115" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18116" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18117" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18118" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18119" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18120" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.031em; left: 0em;"><span id="MathJax-Span-18121" class="mtd"><span id="MathJax-Span-18122" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18123" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18124" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18125" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18126" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18127" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18128" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18129" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18130" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18131" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18132" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18133" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18134" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18135" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18136" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18137" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18138" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18139" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18140" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.986em; vertical-align: -3.067em;"></span></span></nobr></span><script id="MathJax-Element-603" type="math/tex">\begin{array}[t]{l}
+\forall e,attrs.~
+\\
+\qquad entity(e,attrs)
+\\
+\quad\Rightarrow
+typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-604-Frame" class="MathJax"><nobr><span id="MathJax-Span-18141" class="math"><span style="display: inline-block; position: relative; width: 169px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.093em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18142" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18143" class="mtable"><span style="display: inline-block; position: relative; width: 9.521em; height: 0px;"><span style="position: absolute; clip: rect(3.719em, 1000em, 7.604em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 9.521em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18144" class="mtd"><span id="MathJax-Span-18145" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18146" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18147" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18148" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18149" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18150" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18151" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18152" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18153" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18154" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18155" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18156" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.238em; left: 0em;"><span id="MathJax-Span-18157" class="mtd"><span id="MathJax-Span-18158" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18159" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18160" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18161" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18162" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18163" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18164" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18165" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18166" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18167" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18168" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18169" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18170" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18172" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18173" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18174" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.096em; left: 0em;"><span id="MathJax-Span-18175" class="mtd"><span id="MathJax-Span-18176" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18177" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18178" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18179" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18180" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18181" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18182" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18183" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18184" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18185" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18187" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18188" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18189" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18190" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18191" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18192" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18193" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18194" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.055em; vertical-align: -3.137em;"></span></span></nobr></span><script id="MathJax-Element-604" type="math/tex">\begin{array}[t]{l}
+\forall ag,attrs.~
+\\
+\qquad agent(ag,attrs)
+\\
+\quad\Rightarrow
+typeOf(ag,agent)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-605-Frame" class="MathJax"><nobr><span id="MathJax-Span-18195" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.037em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18196" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18197" class="mtable"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.49em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18198" class="mtd"><span id="MathJax-Span-18199" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18200" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18201" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18202" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18203" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18204" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18205" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18206" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18207" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18209" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18210" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18211" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18212" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18213" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18214" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18215" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18216" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18217" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.719em, 1000em, 2.951em, -0.526em); top: -1.294em; left: 0em;"><span id="MathJax-Span-18218" class="mtd"><span id="MathJax-Span-18219" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18220" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18221" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18222" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18223" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18224" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18225" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18226" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18227" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18228" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18229" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18230" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18231" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18232" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18233" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18234" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18235" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18236" class="msubsup"><span style="display: inline-block; position: relative; width: 0.7em; height: 0px;"><span style="position: absolute; clip: rect(1.849em, 1000em, 2.756em, -0.488em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18237" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.274em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18238" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18239" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18240" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18241" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18242" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18243" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18244" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18245" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.04em; left: 0em;"><span id="MathJax-Span-18246" class="mtd"><span id="MathJax-Span-18247" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18248" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18249" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18250" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18251" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18252" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18253" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18254" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18255" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18256" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18257" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18258" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18259" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18260" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18261" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18262" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18263" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18264" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18265" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18266" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18267" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.995em; vertical-align: -3.077em;"></span></span></nobr></span><script id="MathJax-Element-605" type="math/tex">\begin{array}[t]{l}
+\forall a,t_1,t_2,attrs.~
+\\
+\qquad activity(a,t_1,t_2,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-606-Frame" class="MathJax"><nobr><span id="MathJax-Span-18268" class="math"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.006em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18269" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18270" class="mtable"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.4em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18271" class="mtd"><span id="MathJax-Span-18272" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18273" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18274" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18275" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18276" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18277" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18278" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18279" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18280" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18281" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18282" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18283" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18284" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18285" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18286" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18287" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18288" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-18289" class="mtd"><span id="MathJax-Span-18290" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18291" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18292" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18293" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18294" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18295" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18296" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18297" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18298" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18299" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18300" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18301" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18302" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18303" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18305" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18306" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18307" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18308" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18309" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18310" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.009em; left: 0em;"><span id="MathJax-Span-18311" class="mtd"><span id="MathJax-Span-18312" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18313" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18314" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18316" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18317" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18318" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18319" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18320" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18321" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18322" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18323" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18324" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18325" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18326" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18327" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18328" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18329" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18330" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18331" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18332" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18333" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18334" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18335" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18336" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18337" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18338" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18339" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18340" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18341" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18342" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18343" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18344" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18345" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18346" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18347" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18348" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18349" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.962em; vertical-align: -3.044em;"></span></span></nobr></span><script id="MathJax-Element-606" type="math/tex">\begin{array}[t]{l}
+\forall u,a,e,t,attrs.~
+\\
+\qquad used(u,a,e,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-607-Frame" class="MathJax"><nobr><span id="MathJax-Span-18350" class="math"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.1em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18351" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18352" class="mtable"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(3.719em, 1000em, 7.611em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18353" class="mtd"><span id="MathJax-Span-18354" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18355" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18356" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18357" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18358" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18359" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18360" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18361" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18362" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18363" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18364" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18365" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18366" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18367" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18368" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18369" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18370" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-18371" class="mtd"><span id="MathJax-Span-18372" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18373" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18374" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18375" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18376" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18377" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18378" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18379" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18380" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18381" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18382" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18386" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18387" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18388" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18389" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18390" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18391" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18392" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18393" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18394" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18395" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18396" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18397" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18398" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18399" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18400" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18401" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18402" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.103em; left: 0em;"><span id="MathJax-Span-18403" class="mtd"><span id="MathJax-Span-18404" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18405" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18406" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18407" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18408" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18409" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18410" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18411" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18412" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18413" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18414" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18415" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18416" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18417" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18418" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18419" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18420" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18421" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18422" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18423" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18424" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18425" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18427" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18428" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18429" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18430" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18431" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18432" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18433" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18434" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18435" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18436" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18437" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18438" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18439" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18440" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18441" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.063em; vertical-align: -3.144em;"></span></span></nobr></span><script id="MathJax-Element-607" type="math/tex">\begin{array}[t]{l}
+\forall g,a,e,t,attrs.~
+\\
+\qquad wasGeneratedBy(g,e,a,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-608-Frame" class="MathJax"><nobr><span id="MathJax-Span-18442" class="math"><span style="display: inline-block; position: relative; width: 335px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.102em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18443" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18444" class="mtable"><span style="display: inline-block; position: relative; width: 19.217em; height: 0px;"><span style="position: absolute; clip: rect(3.703em, 1000em, 7.613em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.217em; height: 0px;"><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18445" class="mtd"><span id="MathJax-Span-18446" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18447" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18448" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18449" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18450" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18451" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18452" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18453" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18454" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18455" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18456" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18457" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18458" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18459" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18460" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18462" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18463" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18464" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18465" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18466" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18467" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18468" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.23em; left: 0em;"><span id="MathJax-Span-18469" class="mtd"><span id="MathJax-Span-18470" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18471" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18472" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18473" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18474" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18475" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18476" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18477" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18478" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18479" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18480" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18481" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18482" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18483" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18484" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18485" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18486" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18487" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18488" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18489" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18490" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18491" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18492" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18493" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18494" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18495" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18496" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18497" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18498" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18499" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18500" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18501" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18502" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18503" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18504" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18505" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.105em; left: 0em;"><span id="MathJax-Span-18506" class="mtd"><span id="MathJax-Span-18507" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18508" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18509" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18510" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18511" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18512" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18513" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18514" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18515" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18516" class="mo">(</span><span id="MathJax-Span-18517" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18518" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18519" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18520" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18521" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18522" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18523" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18524" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18525" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18526" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18527" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18528" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18529" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18530" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18531" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18532" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18533" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18534" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18535" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18536" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18537" class="mo">(</span><span id="MathJax-Span-18538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18539" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18540" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18541" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18542" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18543" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18544" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18545" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18546" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18547" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18548" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18549" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18550" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.065em; vertical-align: -3.146em;"></span></span></nobr></span><script id="MathJax-Element-608" type="math/tex">\begin{array}[t]{l}
+\forall inf,a_2,a_1,t,attrs.~
+\\
+\qquad wasInformedBy(inf,a_2,a_1,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a_1,activity) \wedge typeOf(a_2,activity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-609-Frame" class="MathJax"><nobr><span id="MathJax-Span-18551" class="math"><span style="display: inline-block; position: relative; width: 468px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.044em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18552" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18553" class="mtable"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.497em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18554" class="mtd"><span id="MathJax-Span-18555" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18556" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18557" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18558" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18559" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18560" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18561" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18562" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18563" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18564" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18565" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18566" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18567" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18568" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18569" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18570" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18571" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18572" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18573" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18574" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18575" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18576" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18578" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18579" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18580" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18581" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-18582" class="mtd"><span id="MathJax-Span-18583" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18584" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18585" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18586" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18587" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18588" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18589" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18590" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18591" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18592" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18593" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18594" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18595" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18596" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18597" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18598" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18599" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18600" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18601" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18603" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18604" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18605" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18606" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18607" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18608" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18609" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18610" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18611" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18612" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18613" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18614" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18615" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18616" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18617" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18618" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18619" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18620" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18621" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.047em; left: 0em;"><span id="MathJax-Span-18622" class="mtd"><span id="MathJax-Span-18623" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18624" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18625" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18626" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18627" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18628" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18630" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18631" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18632" class="mo">(</span><span id="MathJax-Span-18633" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18634" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18635" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18636" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18637" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18638" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18639" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18640" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18641" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18642" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18643" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18644" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18645" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18646" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18647" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18648" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18649" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18651" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18652" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18653" class="mo">(</span><span id="MathJax-Span-18654" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18655" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18656" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18657" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18658" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18659" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18660" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18661" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18662" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18663" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18664" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18665" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18666" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18667" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18668" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18669" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18670" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18671" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18672" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18673" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18674" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18675" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18676" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18677" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18678" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18679" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18680" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18681" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18682" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18683" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.003em; vertical-align: -3.084em;"></span></span></nobr></span><script id="MathJax-Element-609" type="math/tex">\begin{array}[t]{l}
+\forall start,a_2,e,a_1,t,attrs.~
+\\
+\qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-610-Frame" class="MathJax"><nobr><span id="MathJax-Span-18684" class="math"><span style="display: inline-block; position: relative; width: 468px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.044em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18685" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18686" class="mtable"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.497em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 26.986em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18687" class="mtd"><span id="MathJax-Span-18688" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18689" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18690" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18691" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18692" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18693" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18694" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18695" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18696" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18697" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18698" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18699" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18700" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18701" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18702" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18703" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18704" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18705" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18706" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18707" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18708" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18709" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18710" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18711" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18712" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-18713" class="mtd"><span id="MathJax-Span-18714" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18715" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18716" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18717" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18718" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18719" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18720" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18721" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18722" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18723" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18724" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18725" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18726" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18727" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18728" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18729" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18732" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18733" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18734" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18735" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18736" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18737" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18738" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18739" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18740" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18741" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18742" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18743" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18744" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18745" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18746" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18747" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18748" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.047em; left: 0em;"><span id="MathJax-Span-18749" class="mtd"><span id="MathJax-Span-18750" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18751" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18752" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18753" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18754" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18755" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18756" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18757" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18758" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18759" class="mo">(</span><span id="MathJax-Span-18760" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18761" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18762" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18763" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18764" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18765" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18766" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18767" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18768" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18769" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18770" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18771" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18772" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18773" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18774" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18775" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18776" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18777" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18778" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18779" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18780" class="mo">(</span><span id="MathJax-Span-18781" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18782" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18783" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18784" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18785" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18786" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18787" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18788" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18789" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18790" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18791" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18792" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18793" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18794" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18795" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18796" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18797" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18799" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18800" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18801" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18802" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18803" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18804" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18805" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18806" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18807" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18808" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18809" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18810" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.003em; vertical-align: -3.084em;"></span></span></nobr></span><script id="MathJax-Element-610" type="math/tex">\begin{array}[t]{l}
+\forall end,a_2,e,a_1,t,attrs.~
+\\
+\qquad wasEndedBy(end,a_2,e,a_1,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-611-Frame" class="MathJax"><nobr><span id="MathJax-Span-18811" class="math"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.035em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18812" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18813" class="mtable"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.488em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.523em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18814" class="mtd"><span id="MathJax-Span-18815" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18816" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18817" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18818" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18819" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18820" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18821" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18822" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18823" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18824" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18825" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18826" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18827" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18828" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18829" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18830" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18831" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18832" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18833" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-18834" class="mtd"><span id="MathJax-Span-18835" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18836" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18837" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18838" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18839" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18840" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18841" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18842" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18843" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18844" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18845" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18846" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18847" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18848" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18849" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18850" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18851" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18852" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18853" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18854" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18855" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18856" class="mi">v</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18857" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18858" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18859" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18860" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18861" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18862" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18863" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18864" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18865" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18866" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18867" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18868" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18869" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.038em; left: 0em;"><span id="MathJax-Span-18870" class="mtd"><span id="MathJax-Span-18871" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-18872" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18873" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-18874" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18875" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18876" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18877" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18878" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18879" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18880" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18881" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18882" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18883" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18884" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18885" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18886" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18887" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18888" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18889" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18890" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18891" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18892" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18893" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18894" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18895" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18896" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18897" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18898" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18899" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18900" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18901" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18902" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18903" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18905" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18906" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18907" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18908" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.993em; vertical-align: -3.075em;"></span></span></nobr></span><script id="MathJax-Element-611" type="math/tex">\begin{array}[t]{l}
+\forall inv,a,e,t,attrs.~
+\\
+\qquad wasInvalidatedBy(inv,e,a,t,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-612-Frame" class="MathJax"><nobr><span id="MathJax-Span-18909" class="math"><span style="display: inline-block; position: relative; width: 631px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.17em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-18910" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-18911" class="mtable"><span style="display: inline-block; position: relative; width: 36.507em; height: 0px;"><span style="position: absolute; clip: rect(3.756em, 1000em, 7.74em, -0.526em); top: -4.614em; left: 0em;"><span style="display: inline-block; position: relative; width: 36.507em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-18912" class="mtd"><span id="MathJax-Span-18913" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-18914" class="mi">∀</span><span style="font-family: STIXGeneral; 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height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18921" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18922" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18923" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18924" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18925" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18926" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18927" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18928" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18929" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18930" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18931" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-18932" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18933" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18934" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18935" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-18936" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18937" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18939" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18940" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18941" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-18942" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-18943" class="mtd"><span id="MathJax-Span-18944" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-18945" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18946" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18947" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18948" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18949" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18950" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18951" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18952" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18953" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18954" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18955" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18956" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18957" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18958" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18959" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18960" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18961" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18962" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18963" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18964" class="mo">(</span><span id="MathJax-Span-18965" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18966" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18967" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18968" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18969" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18970" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18971" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18972" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18973" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18974" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18975" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18976" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18977" class="mo">(</span><span id="MathJax-Span-18978" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18979" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-18980" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-18981" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-18982" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-18983" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18984" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18985" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18986" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18987" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18988" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18989" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18990" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18991" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18992" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18993" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18994" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18995" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18996" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-18997" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18998" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-18999" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19000" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19001" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19002" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19003" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19004" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19005" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19006" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19007" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19008" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19009" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19010" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19011" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19012" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19013" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19014" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19015" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.484em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19016" class="mi">u</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19017" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19018" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19019" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19020" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19021" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19022" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19023" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19024" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.174em; left: 0em;"><span id="MathJax-Span-19025" class="mtd"><span id="MathJax-Span-19026" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19027" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19028" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19029" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19030" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19031" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19032" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19033" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19034" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19035" class="mo">(</span><span id="MathJax-Span-19036" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19037" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19038" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19039" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19040" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19041" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19042" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19043" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19044" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19045" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19046" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19047" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19048" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19049" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19050" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19051" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19052" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19053" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19054" class="mo">(</span><span id="MathJax-Span-19055" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19056" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19057" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19058" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19059" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19060" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19061" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19062" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19063" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19064" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19065" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19066" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19067" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19068" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19069" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19070" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19071" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19072" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19073" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19074" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19075" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19076" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19077" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19078" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19079" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19080" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19081" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19082" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19083" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19085" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19086" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.614em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.138em; vertical-align: -3.22em;"></span></span></nobr></span><script id="MathJax-Element-612" type="math/tex">\begin{array}[t]{l}
+\forall id,e_2,e_1,a,g_2,u_1,attrs.~
+\\
+\qquad notNull(a) \wedge notNull(g_2) \wedge notNull(u_1) \wedge wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)
+\\
+\quad\Rightarrow
+typeOf(e_2,entity) \wedge typeOf(e_1,activity) \wedge typeOf(a,activity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-613-Frame" class="MathJax"><nobr><span id="MathJax-Span-19087" class="math"><span style="display: inline-block; position: relative; width: 333px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.015em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19088" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19089" class="mtable"><span style="display: inline-block; position: relative; width: 19.1em; height: 0px;"><span style="position: absolute; clip: rect(3.639em, 1000em, 7.468em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 19.1em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19090" class="mtd"><span id="MathJax-Span-19091" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19092" class="mi">∀</span><span style="font-family: STIXGeneral; 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top: -1.287em; left: 0em;"><span id="MathJax-Span-19111" class="mtd"><span id="MathJax-Span-19112" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19113" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19114" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19115" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19116" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19117" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19118" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19119" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-19129" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19130" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19131" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19132" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19133" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19134" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19135" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19136" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19137" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19138" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19139" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19140" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19141" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19142" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19143" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19144" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19145" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19146" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19147" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19148" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19149" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19150" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19151" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.018em; left: 0em;"><span id="MathJax-Span-19152" class="mtd"><span id="MathJax-Span-19153" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19154" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19155" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19156" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19157" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19158" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19159" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19160" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19161" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19162" class="mo">(</span><span id="MathJax-Span-19163" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19164" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19165" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19166" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19167" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19168" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19169" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19170" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19172" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19173" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19174" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19175" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19176" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19177" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19178" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19179" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19180" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19181" class="mo">(</span><span id="MathJax-Span-19182" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19183" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19184" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19185" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19186" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19187" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19188" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19189" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19190" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19191" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19192" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19193" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19194" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.972em; vertical-align: -3.053em;"></span></span></nobr></span><script id="MathJax-Element-613" type="math/tex">\begin{array}[t]{l}
+\forall id,e_2,e_1,attrs.~
+\\
+\qquad wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)
+\\
+\quad\Rightarrow
+typeOf(e_2,entity) \wedge typeOf(e_1,activity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-614-Frame" class="MathJax"><nobr><span id="MathJax-Span-19195" class="math"><span style="display: inline-block; position: relative; width: 302px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.1em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19196" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19197" class="mtable"><span style="display: inline-block; position: relative; width: 17.29em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.611em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.29em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19198" class="mtd"><span id="MathJax-Span-19199" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19200" class="mi">∀</span><span style="font-family: STIXGeneral; 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overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19225" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19226" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19227" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19228" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19230" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19231" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19232" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19233" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19234" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19235" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19236" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19237" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19238" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19239" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19240" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19241" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19242" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19243" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19244" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19245" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19246" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19247" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19248" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.103em; left: 0em;"><span id="MathJax-Span-19249" class="mtd"><span id="MathJax-Span-19250" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19251" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19252" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19253" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19254" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19255" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19256" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19257" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19258" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19259" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19260" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19261" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19262" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19263" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19264" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19265" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19266" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19267" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19268" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19269" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19270" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19271" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19272" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19273" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19274" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19275" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19276" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19277" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19278" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19279" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19280" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19281" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19282" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19283" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19284" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19285" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.063em; vertical-align: -3.144em;"></span></span></nobr></span><script id="MathJax-Element-614" type="math/tex">\begin{array}[t]{l}
+\forall id,e,ag,attrs.~
+\\
+\qquad wasAttributedTo(id,e,ag,attrs)
+\\
+\quad\Rightarrow
+typeOf(e,entity) \wedge typeOf(ag,agent)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-615-Frame" class="MathJax"><nobr><span id="MathJax-Span-19286" class="math"><span style="display: inline-block; position: relative; width: 454px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.105em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19287" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19288" class="mtable"><span style="display: inline-block; position: relative; width: 26.168em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.616em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 26.168em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19289" class="mtd"><span id="MathJax-Span-19290" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19291" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19292" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19293" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19294" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19295" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19296" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19297" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19298" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19299" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19300" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19301" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19302" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19303" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19304" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19305" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19306" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19307" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19308" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19309" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-19310" class="mtd"><span id="MathJax-Span-19311" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19312" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19313" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19314" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19315" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19316" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19317" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19318" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19319" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19320" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19321" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19322" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19323" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19324" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19325" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19326" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19327" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19328" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19329" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19330" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19331" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19332" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19333" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19334" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19335" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19336" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19337" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19338" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19339" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19340" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19341" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19342" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19343" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19344" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19345" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19346" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19347" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19348" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19349" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19350" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19351" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19352" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19353" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19354" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19355" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19356" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19357" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19358" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19359" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-19360" class="mtd"><span id="MathJax-Span-19361" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19362" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19363" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19364" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19365" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19366" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19367" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19368" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19369" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19370" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19371" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19372" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19373" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19374" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19375" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19376" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19377" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19378" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19379" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19380" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19381" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19382" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19383" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19384" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19385" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19386" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19387" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19388" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19389" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19390" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19391" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19392" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19393" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19394" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19395" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19396" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19397" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19398" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19399" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19400" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19401" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19402" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19403" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19404" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19405" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19406" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19407" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19408" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19409" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19410" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19411" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19412" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19413" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19414" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19415" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19416" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.068em; vertical-align: -3.149em;"></span></span></nobr></span><script id="MathJax-Element-615" type="math/tex">\begin{array}[t]{l}
+\forall id,a,ag,pl,attrs.~
+\\
+\qquad notNull(pl) \wedge wasAssociatedWith(id,a,ag,pl,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity) \wedge typeOf(ag,agent) \wedge typeOf(pl,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-616-Frame" class="MathJax"><nobr><span id="MathJax-Span-19417" class="math"><span style="display: inline-block; position: relative; width: 315px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.1em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19418" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19419" class="mtable"><span style="display: inline-block; position: relative; width: 18.049em; height: 0px;"><span style="position: absolute; clip: rect(3.698em, 1000em, 7.611em, -0.526em); top: -4.556em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.049em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19420" class="mtd"><span id="MathJax-Span-19421" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19422" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19423" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19424" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19425" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19426" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19427" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19428" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19429" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19430" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19431" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19432" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19433" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19434" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19435" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19436" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19437" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-19438" class="mtd"><span id="MathJax-Span-19439" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19440" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19441" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19442" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19443" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19444" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19445" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19446" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19447" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19448" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19449" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19450" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19451" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19452" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19454" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19455" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19456" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19457" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19458" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19459" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19460" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19461" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19462" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19463" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19464" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19465" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19466" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19467" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19468" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19469" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19470" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19471" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19472" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19473" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19474" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.103em; left: 0em;"><span id="MathJax-Span-19475" class="mtd"><span id="MathJax-Span-19476" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19477" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19478" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19479" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19480" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19481" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19482" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19483" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19484" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19485" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19486" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19487" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19488" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19489" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19490" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19491" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19492" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19493" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19494" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19495" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19496" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19497" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19498" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19499" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19500" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19501" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19502" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19503" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19504" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19505" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19506" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19507" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19508" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19509" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19510" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19511" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19512" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19513" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.556em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.063em; vertical-align: -3.144em;"></span></span></nobr></span><script id="MathJax-Element-616" type="math/tex">\begin{array}[t]{l}
+\forall id,a,ag,attrs.~
+\\
+\qquad wasAssociatedWith(id,a,ag,-,attrs)
+\\
+\quad\Rightarrow
+typeOf(a,activity) \wedge typeOf(ag,agent)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-617-Frame" class="MathJax"><nobr><span id="MathJax-Span-19514" class="math"><span style="display: inline-block; position: relative; width: 472px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.205em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19515" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19516" class="mtable"><span style="display: inline-block; position: relative; width: 27.22em; height: 0px;"><span style="position: absolute; clip: rect(3.815em, 1000em, 7.833em, -0.526em); top: -4.673em; left: 0em;"><span style="display: inline-block; position: relative; width: 27.22em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19517" class="mtd"><span id="MathJax-Span-19518" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19519" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19520" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19521" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19522" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19523" class="mi">a</span><span id="MathJax-Span-19524" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19525" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19526" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19527" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19528" class="mi">a</span><span id="MathJax-Span-19529" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19530" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19531" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19532" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19533" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19534" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19535" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19536" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19537" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19538" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19539" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19540" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19541" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.987em, -0.526em); top: -1.196em; left: 0em;"><span id="MathJax-Span-19542" class="mtd"><span id="MathJax-Span-19543" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19544" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19545" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19546" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19547" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19548" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19550" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19551" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19552" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19553" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19554" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19555" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19556" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19557" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19558" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19559" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19560" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19561" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19562" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19563" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19564" class="mi">a</span><span id="MathJax-Span-19565" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19566" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19567" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19568" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19569" class="mi">a</span><span id="MathJax-Span-19570" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19571" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19572" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19573" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19574" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19575" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19576" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19577" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19578" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19579" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19580" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19581" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.987em, -0.526em); top: 0.174em; left: 0em;"><span id="MathJax-Span-19582" class="mtd"><span id="MathJax-Span-19583" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19584" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19585" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19586" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19587" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19588" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19589" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19590" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19591" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19592" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19593" class="mi">a</span><span id="MathJax-Span-19594" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19595" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19596" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19597" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19598" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19599" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19600" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19601" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19602" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19603" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19604" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19605" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19606" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19607" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19608" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19609" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19610" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19611" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19612" class="mi">a</span><span id="MathJax-Span-19613" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.518em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19614" class="mi">g</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.861em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19615" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19616" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19617" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19618" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19619" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19620" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19621" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19622" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19623" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19624" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19625" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19626" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19628" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19629" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19630" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19631" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19632" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19633" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19634" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19635" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19636" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19637" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19638" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19639" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19640" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19641" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.673em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.175em; vertical-align: -3.257em;"></span></span></nobr></span><script id="MathJax-Element-617" type="math/tex">\begin{array}[t]{l}
+\forall id,ag_2,ag_1,a,attrs.~
+\\
+\qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
+\\
+\quad\Rightarrow
+typeOf(ag_2,agent) \wedge typeOf(ag_1,agent) \wedge typeOf(a,activity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-618-Frame" class="MathJax"><nobr><span id="MathJax-Span-19642" class="math"><span style="display: inline-block; position: relative; width: 308px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.045em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19643" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19644" class="mtable"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.498em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19645" class="mtd"><span id="MathJax-Span-19646" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19647" class="mi">∀</span><span id="MathJax-Span-19648" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19649" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19650" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19651" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19652" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19653" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19654" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19655" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19656" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-19657" class="mtd"><span id="MathJax-Span-19658" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19659" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19661" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19662" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19663" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19664" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19665" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19666" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19667" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19668" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19669" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19670" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19671" class="mo">(</span><span id="MathJax-Span-19672" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19673" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19674" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19675" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19676" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19677" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19678" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19679" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.048em; left: 0em;"><span id="MathJax-Span-19680" class="mtd"><span id="MathJax-Span-19681" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19682" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19683" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19684" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19685" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19686" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19687" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19688" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19689" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19690" class="mo">(</span><span id="MathJax-Span-19691" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19692" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19693" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19694" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19695" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19696" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19697" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19698" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19699" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19700" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19701" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19702" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19703" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19704" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19705" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19706" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19707" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19708" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19709" class="mo">(</span><span id="MathJax-Span-19710" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19711" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19712" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19713" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19714" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19715" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19716" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19717" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19718" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19719" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19720" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.004em; vertical-align: -3.085em;"></span></span></nobr></span><script id="MathJax-Element-618" type="math/tex">\begin{array}[t]{l}
+\forall e_2,e_1.~
+\\
+\qquad alternateOf(e_2,e_1)
+\\
+\quad\Rightarrow
+typeOf(e_2,entity) \wedge typeOf(e_1,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-619-Frame" class="MathJax"><nobr><span id="MathJax-Span-19721" class="math"><span style="display: inline-block; position: relative; width: 308px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.045em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19722" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19723" class="mtable"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(3.66em, 1000em, 7.498em, -0.526em); top: -4.498em; left: 0em;"><span style="display: inline-block; position: relative; width: 17.64em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19724" class="mtd"><span id="MathJax-Span-19725" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19726" class="mi">∀</span><span id="MathJax-Span-19727" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19728" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19729" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19730" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19731" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19732" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19733" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19734" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19735" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-19736" class="mtd"><span id="MathJax-Span-19737" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19738" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19739" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19740" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19741" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19742" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19743" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19744" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19745" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19746" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19747" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19748" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19749" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19750" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19751" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19752" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19753" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19754" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19755" class="mo">(</span><span id="MathJax-Span-19756" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19757" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19758" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19759" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-19760" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19761" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19762" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19763" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.717em, 1000em, 2.952em, -0.526em); top: 0.048em; left: 0em;"><span id="MathJax-Span-19764" class="mtd"><span id="MathJax-Span-19765" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19766" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19767" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19768" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19769" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19770" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19771" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19772" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19773" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19774" class="mo">(</span><span id="MathJax-Span-19775" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19776" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19777" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19778" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19779" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19780" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19781" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19782" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19783" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19784" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19785" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19786" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19787" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19788" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19789" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19790" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19791" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19792" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19793" class="mo">(</span><span id="MathJax-Span-19794" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19795" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-19796" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19797" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19798" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19799" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19800" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19801" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19802" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19803" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19804" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.498em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.004em; vertical-align: -3.085em;"></span></span></nobr></span><script id="MathJax-Element-619" type="math/tex">\begin{array}[t]{l}
+\forall e_2,e_1.~
+\\
+\qquad specializationOf(e_2,e_1)
+\\
+\quad\Rightarrow
+typeOf(e_2,entity) \wedge typeOf(e_1,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-620-Frame" class="MathJax"><nobr><span id="MathJax-Span-19805" class="math"><span style="display: inline-block; position: relative; width: 374px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.011em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19806" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19807" class="mtable"><span style="display: inline-block; position: relative; width: 21.495em; height: 0px;"><span style="position: absolute; clip: rect(3.602em, 1000em, 7.405em, -0.526em); top: -4.439em; left: 0em;"><span style="display: inline-block; position: relative; width: 21.495em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19808" class="mtd"><span id="MathJax-Span-19809" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19810" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19811" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19812" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19813" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19814" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-19815" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-19816" class="mtd"><span id="MathJax-Span-19817" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-19818" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19819" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19820" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19821" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19822" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19823" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19824" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19825" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19826" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19827" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19828" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19829" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19830" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19831" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19832" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: 0.014em; left: 0em;"><span id="MathJax-Span-19833" class="mtd"><span id="MathJax-Span-19834" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19835" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19836" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19837" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19838" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19839" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19840" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19841" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19842" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19843" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19844" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19845" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19846" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19847" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19848" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19849" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-19850" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19851" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19852" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19853" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19854" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19855" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19856" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19857" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19858" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19859" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19860" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19861" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-19862" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-19863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19864" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19865" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19866" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19867" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19868" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19869" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19870" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19871" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19872" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19873" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19874" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19875" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19876" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19877" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19878" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.439em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.967em; vertical-align: -3.049em;"></span></span></nobr></span><script id="MathJax-Element-620" type="math/tex">\begin{array}[t]{l}
+\forall c,e.~
+\\
+\qquad hadMember(c,e)
+\\
+\quad\Rightarrow
+typeOf(c,prov:Collection) \wedge typeOf(e,entity)
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-621-Frame" class="MathJax"><nobr><span id="MathJax-Span-19879" class="math"><span style="display: inline-block; position: relative; width: 633px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.966em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-19880" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-19881" class="mtable"><span style="display: inline-block; position: relative; width: 36.624em; height: 0px;"><span style="position: absolute; clip: rect(3.544em, 1000em, 7.302em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 36.624em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.756em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-19882" class="mtd"><span id="MathJax-Span-19883" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-19884" class="mi">∀</span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-19927" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19928" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19929" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19930" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19931" class="mo">]</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19932" class="mo">)</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19933" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -0.031em; left: 0em;"><span id="MathJax-Span-19934" class="mtd"><span id="MathJax-Span-19935" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-19936" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19937" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19938" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19939" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19940" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19941" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19942" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19943" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-19944" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19945" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-19946" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-19947" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19948" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19949" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19950" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19951" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; 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font-style: italic;" id="MathJax-Span-19993" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-19994" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-19995" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19996" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19997" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19998" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19999" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20000" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20001" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20002" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20003" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20004" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20005" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20006" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20007" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20008" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20009" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20010" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.919em; vertical-align: -3.001em;"></span></span></nobr></span><script id="MathJax-Element-621" type="math/tex">\begin{array}[t]{l}
+\forall c.~
+\\
+\qquad entity(c,[prov:type = prov:emptyCollection]))
+\\
+\quad\Rightarrow
+typeOf(c,entity) \wedge typeOf(c,prov:Collection) \wedge typeOf(c,prov:EmptyCollection)
+\end{array}</script></li></ol></div>
+<div class="proof">
+ <p>Each typing constraint follows immediately from well-formedness
+ criteria marked [WF] in the corresponding semantics for formulas.
+ </p>
+ </div>
+</section>
+
+<section id="impossibility-constraints">
+<h4><span class="secno">5.2.4 </span>Impossibility constraints</h4>
+
+<div class="constraint" number="51" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a href="#impossible-unspecified-derivation-generation-use" class="internalDFN">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-622-Frame" class="MathJax"><nobr><span id="MathJax-Span-20011" class="math"><span style="display: inline-block; position: relative; width: 422px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20012" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20013" class="mtable"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.279em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20014" class="mtd"><span id="MathJax-Span-20015" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20016" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20017" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20018" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20019" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20020" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20021" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20022" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20023" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20024" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20025" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20026" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20027" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20028" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20029" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20030" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20031" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20032" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20033" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20034" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20035" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20036" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-20037" class="mtd"><span id="MathJax-Span-20038" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20039" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20040" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20041" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20042" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20043" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20044" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20045" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20046" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20047" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20048" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20049" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20050" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20051" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20052" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20053" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20054" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20055" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20056" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20057" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20058" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20059" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20060" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20061" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20062" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20063" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20064" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20065" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20066" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20067" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20068" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20069" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20070" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20071" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20072" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20073" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20074" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20075" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20076" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20077" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20078" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20079" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20080" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20081" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20082" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20083" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20084" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20085" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20086" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20087" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20088" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-20089" class="mtd"><span id="MathJax-Span-20090" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20091" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20092" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20093" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20094" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20095" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20096" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20097" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-622" type="math/tex">\begin{array}[t]{l}
+\forall id,e_1,e_2,g,attrs.~
+\\
+\qquad notNull(g) \wedge wasDerivedFrom(id,e_2,e_1,-,g,-,attrs)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-623-Frame" class="MathJax"><nobr><span id="MathJax-Span-20098" class="math"><span style="display: inline-block; position: relative; width: 422px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.013em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20099" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20100" class="mtable"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.136em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.299em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.895em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20101" class="mtd"><span id="MathJax-Span-20102" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20103" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20104" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20105" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20106" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20107" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20108" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20109" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20110" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20111" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20112" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20113" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20114" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20115" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20116" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20117" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20118" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20119" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20120" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20121" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20122" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20123" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.287em; left: 0em;"><span id="MathJax-Span-20124" class="mtd"><span id="MathJax-Span-20125" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20126" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20127" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20128" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20129" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20130" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20131" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20132" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20133" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20134" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20135" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20136" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20137" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20138" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20139" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20140" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20141" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20142" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20143" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20144" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20145" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20146" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20147" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20148" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20149" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20150" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20151" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20152" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20153" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20154" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20155" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20156" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20157" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20158" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20159" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20160" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20161" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20162" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20163" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20164" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20165" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20166" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20167" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20168" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20169" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20170" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20171" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20172" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20173" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20174" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20175" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.023em; left: 0em;"><span id="MathJax-Span-20176" class="mtd"><span id="MathJax-Span-20177" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20178" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20179" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20180" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20181" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20182" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20183" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20184" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.97em; vertical-align: -3.051em;"></span></span></nobr></span><script id="MathJax-Element-623" type="math/tex">\begin{array}[t]{l}
+\forall id,e_1,e_2,u,attrs.~
+\\
+\qquad notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,-,u,attrs)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-624-Frame" class="MathJax"><nobr><span id="MathJax-Span-20185" class="math"><span style="display: inline-block; position: relative; width: 511px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.098em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20186" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20187" class="mtable"><span style="display: inline-block; position: relative; width: 29.498em; height: 0px;"><span style="position: absolute; clip: rect(3.523em, 1000em, 7.279em, -0.526em); top: -4.381em; left: 0em;"><span style="display: inline-block; position: relative; width: 29.498em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20188" class="mtd"><span id="MathJax-Span-20189" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20190" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20191" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20192" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20193" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20194" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20195" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20196" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20197" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20198" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20199" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20200" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20201" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20202" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20203" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20204" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20205" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20206" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20207" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20208" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20209" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20210" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20211" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20212" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.951em, -0.526em); top: -1.231em; left: 0em;"><span id="MathJax-Span-20213" class="mtd"><span id="MathJax-Span-20214" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20215" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20216" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20217" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20218" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20219" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20220" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20221" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20222" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20223" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20224" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20225" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20226" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20227" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20228" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20229" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20230" class="mi">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.06em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20231" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20232" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20233" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20234" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20235" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20236" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20237" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20238" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20239" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20240" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20241" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20242" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20243" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20244" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20245" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20246" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20247" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20248" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20249" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20250" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20251" class="mi">m</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20252" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20253" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20254" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20255" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20256" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20257" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20258" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20259" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20260" class="msubsup"><span style="display: inline-block; position: relative; width: 0.893em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.495em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20261" class="mi">e</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.467em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20262" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20263" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20264" class="mo">−</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20265" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20266" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20267" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20268" class="mi">u</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20269" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20270" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20271" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20272" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20273" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20274" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20275" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.108em; left: 0em;"><span id="MathJax-Span-20276" class="mtd"><span id="MathJax-Span-20277" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20278" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20279" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20280" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20281" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20282" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20283" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20284" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.06em; vertical-align: -3.142em;"></span></span></nobr></span><script id="MathJax-Element-624" type="math/tex">\begin{array}[t]{l}
+\forall id,e_1,e_2,g,u,attrs.~
+\\
+\qquad notNull(g) \wedge notNull(u) \wedge wasDerivedFrom(id,e_2,e_1,-,g,u,attrs)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></li></ol></div>
+<div class="proof">
+ <p>Each part follows from the fact that the semantics of
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-625-Frame" class="MathJax"><nobr><span id="MathJax-Span-20285" class="math"><span style="display: inline-block; position: relative; width: 121px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.763em, -0.511em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20286" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20287" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20288" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20289" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20290" class="mi">D</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20291" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20292" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20293" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20294" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20295" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20296" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20297" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20298" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20299" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20300" class="mi">m</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.875em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-625" type="math/tex">wasDerivedFrom</script> only allows formulas to hold when either all three
+ of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-626-Frame" class="MathJax"><nobr><span id="MathJax-Span-20301" class="math"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.951em, -0.509em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20302" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20303" class="mi">a</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20304" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20305" class="mi">g</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20306" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20307" class="mi">u</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.817em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-626" type="math/tex">a,g,u</script> are <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-627-Frame" class="MathJax"><nobr><span id="MathJax-Span-20308" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(2.109em, 1000em, 2.625em, -0.462em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20309" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20310" class="mo">−</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.303em; vertical-align: 0.066em;"></span></span></nobr></span><script id="MathJax-Element-627" type="math/tex">-</script> (denoting <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-628-Frame" class="MathJax"><nobr><span id="MathJax-Span-20311" class="math"><span style="display: inline-block; position: relative; width: 12px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.745em, -0.478em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20312" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20313" class="mi">⊥</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.833em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-628" type="math/tex">\bot</script>) or none of them are.</p>
+ </div>
+<div class="constraint" number="52" id="impossible-specialization-reflexive"><div class="ruleTitle"><a href="#impossible-specialization-reflexive" class="internalDFN">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-629-Frame" class="MathJax"><nobr><span id="MathJax-Span-20314" class="math"><span style="display: inline-block; position: relative; width: 194px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.96em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20315" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20316" class="mtable"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(3.427em, 1000em, 7.024em, -0.526em); top: -4.264em; left: 0em;"><span style="display: inline-block; position: relative; width: 10.981em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.756em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20317" class="mtd"><span id="MathJax-Span-20318" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20319" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20320" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20321" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20322" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-20323" class="mtd"><span id="MathJax-Span-20324" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20325" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20326" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20327" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20328" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20329" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20330" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20331" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20332" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20333" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20334" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20335" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20336" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20337" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20338" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20339" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20340" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20341" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20342" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20343" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20344" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20345" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20346" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: -0.03em; left: 0em;"><span id="MathJax-Span-20347" class="mtd"><span id="MathJax-Span-20348" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20349" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20350" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20351" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20352" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20353" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20354" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20355" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.264em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.913em; vertical-align: -2.994em;"></span></span></nobr></span><script id="MathJax-Element-629" type="math/tex">\begin{array}[t]{l}
+\forall e.~
+\\
+\qquad specializationOf(e,e)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></div>
+<div class="proof">
+ <p>This follows from the fact that in the semantics of
+ <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-630-Frame" class="MathJax"><nobr><span id="MathJax-Span-20356" class="math"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20357" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20358" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20359" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20360" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20361" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20362" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20363" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20364" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20365" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20366" class="mi">z</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20367" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20368" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20369" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20370" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20371" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20372" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20373" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-630" type="math/tex">specializationOf</script>, the two entities denoted by the first and second
+ arguments are required to be distinct.
+ </p>
+ </div>
+<div class="constraint" number="53" id="impossible-property-overlap"><div class="ruleTitle"><a href="#impossible-property-overlap" class="internalDFN">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-631-Frame" class="MathJax"><nobr><span id="MathJax-Span-20374" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20375" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20376" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.597em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-631" type="math/tex">r</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-632-Frame" class="MathJax"><nobr><span id="MathJax-Span-20377" class="math"><span style="display: inline-block; position: relative; width: 1050px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20378" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20379" class="mi">s</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20380" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20381" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20382" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20383" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20384" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20385" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20386" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20387" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20388" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20389" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20390" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20391" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20392" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20393" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20394" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20395" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20396" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20397" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20398" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20399" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20400" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20401" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20402" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20403" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20404" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20405" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20406" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20407" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20408" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20409" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20410" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20411" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20412" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20413" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20414" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20415" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20416" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20417" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20418" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20419" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20420" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20421" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20422" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20423" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20424" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20425" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20426" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20427" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20428" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20429" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20430" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20431" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20432" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20433" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20434" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20435" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20436" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20437" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20438" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20439" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20440" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20441" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20442" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20443" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20444" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20445" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20446" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20447" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20448" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20449" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20450" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20451" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20452" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20453" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20454" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20455" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20456" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20457" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20458" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20459" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20460" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20461" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20462" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20463" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20464" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20465" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20466" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20467" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20468" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20469" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20470" class="mi">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.077em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20471" class="mi">o</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20472" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20473" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20474" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20475" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20476" class="mi">A</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20477" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20478" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20479" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20480" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20481" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20482" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20483" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20484" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20485" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20486" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20487" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20488" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20489" class="mi">h</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20490" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20491" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20492" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20493" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20494" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20495" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20496" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20497" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20498" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20499" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20500" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20501" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20502" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20503" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20504" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20505" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20506" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.077em; vertical-align: -0.284em;"></span></span></nobr></span><script id="MathJax-Element-632" type="math/tex">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-633-Frame" class="MathJax"><nobr><span id="MathJax-Span-20507" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.745em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20508" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20509" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.597em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-633" type="math/tex">r</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-634-Frame" class="MathJax"><nobr><span id="MathJax-Span-20510" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.953em, 1000em, 2.758em, -0.51em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20511" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20512" class="mi">s</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.612em; vertical-align: -0.076em;"></span></span></nobr></span><script id="MathJax-Element-634" type="math/tex">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-635-Frame" class="MathJax"><nobr><span id="MathJax-Span-20513" class="math"><span style="display: inline-block; position: relative; width: 278px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.019em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20514" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20515" class="mtable"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(3.464em, 1000em, 7.142em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 15.888em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.902em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20516" class="mtd"><span id="MathJax-Span-20517" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20518" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20519" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20520" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20521" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20522" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20523" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20524" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20525" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20526" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20527" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20528" class="msubsup"><span style="display: inline-block; position: relative; width: 1.126em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20529" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20530" class="mi">m</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20531" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20532" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20533" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20534" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20535" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20536" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20537" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20538" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20539" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20540" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20541" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20542" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.922em, -0.526em); top: -1.281em; left: 0em;"><span id="MathJax-Span-20543" class="mtd"><span id="MathJax-Span-20544" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20545" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20546" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20547" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20548" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20549" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20550" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20551" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20552" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20553" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20554" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20555" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20556" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20557" class="msubsup"><span style="display: inline-block; position: relative; width: 1.126em; height: 0px;"><span style="position: absolute; clip: rect(1.954em, 1000em, 2.756em, -0.509em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20558" class="mi">a</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20559" class="mi">m</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20560" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20561" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20562" class="mi">s</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20563" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20564" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20565" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20566" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20567" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20568" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20569" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20570" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20571" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20572" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20573" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20574" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20575" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20576" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.029em; left: 0em;"><span id="MathJax-Span-20577" class="mtd"><span id="MathJax-Span-20578" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20579" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20580" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20581" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20582" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20583" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20584" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20585" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.976em; vertical-align: -3.058em;"></span></span></nobr></span><script id="MathJax-Element-635" type="math/tex">\begin{array}[t]{l}
+\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
+\\
+\qquad r(id,a_1,\ldots,a_m) \wedge s(id,b_1,\ldots,b_n)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></div>
+<div class="proof">
+ <p>This follows from the assumption that the different classes of
+ interactions are disjoint sets, characterized by their types.
+ </p>
+ </div>
+<div class="constraint" number="54" id="impossible-object-property-overlap"><div class="ruleTitle"><a href="#impossible-object-property-overlap" class="internalDFN">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-636-Frame" class="MathJax"><nobr><span id="MathJax-Span-20586" class="math"><span style="display: inline-block; position: relative; width: 187px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.715em, 1000em, 2.951em, -0.601em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20587" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20588" class="mi">p</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20589" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20590" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20591" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20592" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20593" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20594" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20595" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20596" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20597" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20598" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20599" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20600" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20601" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20602" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20603" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20604" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20605" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20606" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20607" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20608" class="mi">g</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20609" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20610" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20611" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20612" class="mo">}</span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.073em; vertical-align: -0.283em;"></span></span></nobr></span><script id="MathJax-Element-636" type="math/tex">p \in \{entity,activity,agent\}</script> and each <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-637-Frame" class="MathJax"><nobr><span id="MathJax-Span-20613" class="math"><span style="display: inline-block; position: relative; width: 1050px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.481em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20614" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20615" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20616" class="mo">∈</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20617" class="mo">{</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20618" class="mi">u</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20619" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20620" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20621" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20622" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20623" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20624" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20625" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20626" class="mi">G</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20627" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20628" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20629" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20630" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20631" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20632" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20633" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20634" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20635" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20636" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20637" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20638" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20639" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20640" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20641" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20642" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20643" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20644" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20645" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20646" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20647" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20648" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20649" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20650" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20651" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20652" class="mi">B</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20653" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20654" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20655" class="mi">w</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20656" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20657" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20658" class="mi">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.008em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20659" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20660" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20661" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; 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position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20798" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-20799" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20800" class="mo">,</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20801" class="mo">…</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20802" class="mo">,</span><span style="padding-left: 0.188em;" id="MathJax-Span-20803" class="msubsup"><span style="display: inline-block; position: relative; width: 0.951em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.756em, -0.503em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20804" class="mi">b</span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -1.953em; left: 0.526em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20805" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20806" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.057em; left: 0em;"><span id="MathJax-Span-20807" class="mtd"><span id="MathJax-Span-20808" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20809" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20810" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20811" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20812" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20813" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20814" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20815" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.381em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 4.006em; vertical-align: -3.088em;"></span></span></nobr></span><script id="MathJax-Element-638" type="math/tex">\begin{array}[t]{l}
+\forall id,a_1,\ldots,a_m,b_1,\ldots,b_n.~
+\\
+\qquad p(id,a_1,\ldots,a_m) \wedge r(id,b_1,\ldots,b_n)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></div>
+<div class="proof">
+ <p>This follows from the assumption that interactions are distinct
+ from other objects (entities, activities or agents).
+ </p>
+ </div>
+<div class="constraint" number="55" id="entity-activity-disjoint"><div class="ruleTitle"><a href="#entity-activity-disjoint" class="internalDFN">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-639-Frame" class="MathJax"><nobr><span id="MathJax-Span-20816" class="math"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 4.96em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20817" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20818" class="mtable"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(3.406em, 1000em, 7.024em, -0.526em); top: -4.264em; left: 0em;"><span style="display: inline-block; position: relative; width: 18.107em; height: 0px;"><span style="position: absolute; clip: rect(1.712em, 1000em, 2.758em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20819" class="mtd"><span id="MathJax-Span-20820" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20821" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20822" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20823" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20824" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20825" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.37em; left: 0em;"><span id="MathJax-Span-20826" class="mtd"><span id="MathJax-Span-20827" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20828" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20829" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20830" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20831" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20832" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20833" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20834" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20835" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20836" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20837" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20838" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20839" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20840" class="mi">n</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20841" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20842" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20843" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20844" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20845" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20846" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20847" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20848" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20849" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20850" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20851" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20852" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20853" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20854" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20855" class="mi">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.027em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20856" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20857" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20858" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20859" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20860" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20861" class="mi">v</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20862" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20863" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20864" class="mi">y</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20865" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: -0.03em; left: 0em;"><span id="MathJax-Span-20866" class="mtd"><span id="MathJax-Span-20867" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20868" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20869" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20870" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20871" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20872" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20873" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20874" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.264em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.913em; vertical-align: -2.994em;"></span></span></nobr></span><script id="MathJax-Element-639" type="math/tex">\begin{array}[t]{l}
+\forall id.~
+\\
+\qquad typeOf(id,entity) \wedge typeOf(id,activity)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></div>
+<div class="proof">
+ <p>This follows from the assumption that entities and activities are disjoint.
+ </p>
+ </div>
+<div class="constraint" number="56" id="membership-empty-collection"><div class="ruleTitle"><a href="#membership-empty-collection" class="internalDFN">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-640-Frame" class="MathJax"><nobr><span id="MathJax-Span-20875" class="math"><span style="display: inline-block; position: relative; width: 419px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.069em, 1000em, 5.034em, -0.359em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20876" class="mrow"><span style="padding-right: 0.167em; padding-left: 0.167em;" id="MathJax-Span-20877" class="mtable"><span style="display: inline-block; position: relative; width: 24.124em; height: 0px;"><span style="position: absolute; clip: rect(3.485em, 1000em, 7.157em, -0.526em); top: -4.322em; left: 0em;"><span style="display: inline-block; position: relative; width: 24.124em; height: 0px;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.886em, -0.524em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20878" class="mtd"><span id="MathJax-Span-20879" class="mrow"><span style="font-family: STIXGeneral;" id="MathJax-Span-20880" class="mi">∀</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20881" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20882" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20883" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20884" class="mo">.</span><span style="font-family: STIXGeneral; padding-left: 0.188em;" id="MathJax-Span-20885" class="mtext"> </span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.952em, -0.526em); top: -1.296em; left: 0em;"><span id="MathJax-Span-20886" class="mtd"><span id="MathJax-Span-20887" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 2.25em; display: inline-block; overflow: hidden;" id="MathJax-Span-20888" class="mspace"></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20889" class="mi">h</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20890" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20891" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20892" class="mi">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.039em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20893" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20894" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20895" class="mi">b</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20896" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20897" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20898" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20899" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20900" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20901" class="mi">e</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20902" class="mo">)</span><span style="font-family: STIXGeneral; padding-left: 0.25em;" id="MathJax-Span-20903" class="mo">∧</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.25em;" id="MathJax-Span-20904" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20905" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20906" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20907" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20908" class="mi">O</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20909" class="mi">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.146em;"></span></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20910" class="mo">(</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20911" class="mi">c</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20912" class="mo">,</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.188em;" id="MathJax-Span-20913" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20914" class="mi">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20915" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20916" class="mi">v</span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20917" class="mo">:</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20918" class="mi">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.023em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20919" class="mi">m</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20920" class="mi">p</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20921" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20922" class="mi">y</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20923" class="mi">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.022em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20924" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20925" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20926" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20927" class="mi">e</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20928" class="mi">c</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20929" class="mi">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.018em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20930" class="mi">i</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20931" class="mi">o</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20932" class="mi">n</span><span style="font-family: STIXGeneral;" id="MathJax-Span-20933" class="mo">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; clip: rect(1.712em, 1000em, 2.79em, -0.526em); top: 0.044em; left: 0em;"><span id="MathJax-Span-20934" class="mtd"><span id="MathJax-Span-20935" class="mrow"><span style="height: 0em; vertical-align: 0em; width: 1.125em; display: inline-block; overflow: hidden;" id="MathJax-Span-20936" class="mspace"></span><span style="font-family: STIXGeneral;" id="MathJax-Span-20937" class="mo">⇒</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20938" class="mi">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.034em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20939" class="mi">a</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20940" class="mi">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.001em;"></span></span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20941" class="mi">s</span><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20942" class="mi">e</span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.322em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 3.992em; vertical-align: -3.073em;"></span></span></nobr></span><script id="MathJax-Element-640" type="math/tex">\begin{array}[t]{l}
+\forall c,e.~
+\\
+\qquad hasMember(c,e) \wedge typeOf(c,prov:EmptyCollection)
+\\
+\quad\Rightarrow
+False
+\end{array}</script></div>
+
+</section>
+</section>
+</section>
+
+
+<section id="soundness">
+<!--OddPage--><h2><span class="secno">6. </span>Soundness</h2>
+
+<p>Above we have presented arguments for the soundness of the
+constraints and inferences with respect to the reference semantics.
+This implies the following:
+
+</p><div data-title="Theorem 32 (soundness)" data-count="32" class="theorem" id="soundness"><div class="ruleTitle"><a href="#soundness" class="internalDFN">Theorem 32 (soundness)</a></div>
+ <ol>
+ <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-641-Frame" class="MathJax"><nobr><span id="MathJax-Span-20943" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20944" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20945" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-641" type="math/tex">I</script> is an instance and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-642-Frame" class="MathJax"><nobr><span id="MathJax-Span-20946" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20947" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20948" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20949" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20950" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-642" type="math/tex">W \models I</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-643-Frame" class="MathJax"><nobr><span id="MathJax-Span-20951" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20952" class="mrow"><span id="MathJax-Span-20953" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20954" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20955" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-643" type="math/tex">I'</script> is obtained from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-644-Frame" class="MathJax"><nobr><span id="MathJax-Span-20956" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20957" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20958" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-644" type="math/tex">I</script> by applying one
+ of the PROV inferences, then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-645-Frame" class="MathJax"><nobr><span id="MathJax-Span-20959" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20960" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20961" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20962" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-20963" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20964" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20965" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-645" type="math/tex">W \models I'</script>.</li>
+ <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-646-Frame" class="MathJax"><nobr><span id="MathJax-Span-20966" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20967" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20968" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-646" type="math/tex">I</script> is an instance and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-647-Frame" class="MathJax"><nobr><span id="MathJax-Span-20969" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20970" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20971" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20972" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20973" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-647" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-648-Frame" class="MathJax"><nobr><span id="MathJax-Span-20974" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20975" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20976" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-648" type="math/tex">I</script> has a normal
+ form <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-649-Frame" class="MathJax"><nobr><span id="MathJax-Span-20977" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-20978" class="mrow"><span id="MathJax-Span-20979" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20980" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20981" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-649" type="math/tex">I'</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-650-Frame" class="MathJax"><nobr><span id="MathJax-Span-20982" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20983" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20984" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20985" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-20986" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20987" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-20988" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-650" type="math/tex"> W \models I'</script>.</li>
+ <li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-651-Frame" class="MathJax"><nobr><span id="MathJax-Span-20989" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20990" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20991" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-651" type="math/tex">I</script> is a normal form and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-652-Frame" class="MathJax"><nobr><span id="MathJax-Span-20992" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20993" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20994" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-20995" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-20996" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-652" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-653-Frame" class="MathJax"><nobr><span id="MathJax-Span-20997" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-20998" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-20999" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-653" type="math/tex">I</script> satisfies all of the ordering,
+ typing and impossibility constraints.
+ </li><li>If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-654-Frame" class="MathJax"><nobr><span id="MathJax-Span-21000" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21001" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21002" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21003" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21004" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-654" type="math/tex">W \models I</script> then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-655-Frame" class="MathJax"><nobr><span id="MathJax-Span-21005" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21006" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21007" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-655" type="math/tex">I</script> is valid.</li>
+ <p></p>
+</ol></div>
+<div class="proof">
+ <p>For part 1, the arguments are as in the previous section. </p>
+ <p>For
+ part 2, proceed by induction on a terminating sequence of inference
+ or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-656-Frame" class="MathJax"><nobr><span id="MathJax-Span-21008" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21009" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21010" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-656" type="math/tex">I</script> is in normal form them we are
+ done. If <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-657-Frame" class="MathJax"><nobr><span id="MathJax-Span-21011" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21012" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21013" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-657" type="math/tex">I</script> is not in normal form then if an inference is applicable, then use part 1; if a uniqueness constraint is
+ applicable, then from <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-658-Frame" class="MathJax"><nobr><span id="MathJax-Span-21014" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21015" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21016" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21017" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21018" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-658" type="math/tex">W \models I</script> the uniqueness constraint cannot
+ fail on <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-659-Frame" class="MathJax"><nobr><span id="MathJax-Span-21019" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21020" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21021" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-659" type="math/tex">I</script> and <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-660-Frame" class="MathJax"><nobr><span id="MathJax-Span-21022" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21023" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21024" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21025" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-21026" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21027" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21028" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-660" type="math/tex">W \models I'</script>.</p>
+<p>
+ For part 3, the arguments are as
+ in the previous section for each constraint. </p>
+ <p>Finally, for part 4,
+ suppose <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-661-Frame" class="MathJax"><nobr><span id="MathJax-Span-21029" class="math"><span style="display: inline-block; position: relative; width: 44px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.733em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21030" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21031" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21032" class="mo">⊨</span><span style="font-family: STIXGeneral; font-style: italic; padding-left: 0.313em;" id="MathJax-Span-21033" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.853em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-661" type="math/tex">W \models I</script>. Then <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-662-Frame" class="MathJax"><nobr><span id="MathJax-Span-21034" class="math"><span style="display: inline-block; position: relative; width: 51px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.615em, 1000em, 2.763em, -0.455em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21035" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21036" class="mi">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.073em;"></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-21037" class="mo">⊨</span><span style="padding-left: 0.313em;" id="MathJax-Span-21038" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21039" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21040" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.978em; vertical-align: -0.082em;"></span></span></nobr></span><script id="MathJax-Element-662" type="math/tex">W \models I'</script> where <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-663-Frame" class="MathJax"><nobr><span id="MathJax-Span-21041" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-21042" class="mrow"><span id="MathJax-Span-21043" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21044" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21045" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-663" type="math/tex">I'</script> is the normal
+ form of <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-664-Frame" class="MathJax"><nobr><span id="MathJax-Span-21046" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21047" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21048" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-664" type="math/tex">I</script> by part 2. By part 3, <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-665-Frame" class="MathJax"><nobr><span id="MathJax-Span-21049" class="math"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.09em, 1000em, 2.22em, -0.534em); top: -2.044em; left: 0em;"><span id="MathJax-Span-21050" class="mrow"><span id="MathJax-Span-21051" class="msup"><span style="display: inline-block; position: relative; width: 0.783em; height: 0px;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21052" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span><span style="position: absolute; top: -2.483em; left: 0.474em;"><span style="font-size: 70.7%; font-family: STIXVariants;" id="MathJax-Span-21053" class="mo">′</span><span style="display: inline-block; width: 0px; height: 2.103em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.044em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.959em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-665" type="math/tex">I'</script> satisfies all of the
+ remaining constraints, so <span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-666-Frame" class="MathJax"><nobr><span id="MathJax-Span-21054" class="math"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 107%;"><span style="position: absolute; clip: rect(1.742em, 1000em, 2.745em, -0.534em); top: -2.57em; left: 0em;"><span id="MathJax-Span-21055" class="mrow"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-21056" class="mi">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.051em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.57em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 0.824em; vertical-align: -0.063em;"></span></span></nobr></span><script id="MathJax-Element-666" type="math/tex">I</script> is valid.</p>
+ </div>
+
+
+
+</section>
+
+<section id="acknowledgements" class="appendix">
+ <!--OddPage--><h2><span class="secno">A. </span>Acknowledgements</h2>
+ <p>
+
+This document has been produced by the PROV Working Group, and its contents reflect extensive discussion within the Working Group as a whole.
+ </p>
+<p>Thanks also to Robin Berjon for the ReSPec.js specification writing
+tool and to MathJax for their LaTeX-to-HTML conversion tools, both of
+ which aided in the preparation of this document.</p>
+
+<p>
+Members of the PROV Working Group at the time of publication of this document were:
+
+Ilkay Altintas (Invited expert),
+Reza B'Far (Oracle Corporation),
+Khalid Belhajjame (University of Manchester),
+James Cheney (University of Edinburgh, School of Informatics),
+Sam Coppens (IBBT),
+David Corsar (University of Aberdeen, Computing Science),
+Stephen Cresswell (The National Archives),
+Tom De Nies (IBBT),
+Helena Deus (DERI Galway at the National University of Ireland, Galway, Ireland),
+Simon Dobson (Invited expert),
+Martin Doerr (Foundation for Research and Technology - Hellas(FORTH)),
+Kai Eckert (Invited expert),
+Jean-Pierre EVAIN (European Broadcasting Union, EBU-UER),
+James Frew (Invited expert),
+Irini Fundulaki (Foundation for Research and Technology - Hellas(FORTH)),
+Daniel Garijo (Universidad Politécnica de Madrid),
+Yolanda Gil (Invited expert),
+Ryan Golden (Oracle Corporation),
+Paul Groth (Vrije Universiteit),
+Olaf Hartig (Invited expert),
+David Hau (National Cancer Institute, NCI),
+Sandro Hawke (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="Massachusetts Institute of Technology">MIT</abbr>),
+Jörn Hees (German Research Center for Artificial Intelligence (DFKI) Gmbh),
+Ivan Herman, (<abbr title="World Wide Web Consortium">W3C</abbr>/<abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr>),
+Ralph Hodgson (TopQuadrant),
+Hook Hua (Invited expert),
+Trung Dong Huynh (University of Southampton),
+Graham Klyne (University of Oxford),
+Michael Lang (Revelytix, Inc.),
+Timothy Lebo (Rensselaer Polytechnic Institute),
+James McCusker (Rensselaer Polytechnic Institute),
+Deborah McGuinness (Rensselaer Polytechnic Institute),
+Simon Miles (Invited expert),
+Paolo Missier (School of Computing Science, Newcastle university),
+Luc Moreau (University of Southampton),
+James Myers (Rensselaer Polytechnic Institute),
+Vinh Nguyen (Wright State University),
+Edoardo Pignotti (University of Aberdeen, Computing Science),
+Paulo da Silva Pinheiro (Rensselaer Polytechnic Institute),
+Carl Reed (Open Geospatial Consortium),
+Adam Retter (Invited Expert),
+Christine Runnegar (Invited expert),
+Satya Sahoo (Invited expert),
+David Schaengold (Revelytix, Inc.),
+Daniel Schutzer (FSTC, Financial Services Technology Consortium),
+Yogesh Simmhan (Invited expert),
+Stian Soiland-Reyes (University of Manchester),
+Eric Stephan (Pacific Northwest National Laboratory),
+Linda Stewart (The National Archives),
+Ed Summers (Library of Congress),
+Maria Theodoridou (Foundation for Research and Technology - Hellas(FORTH)),
+Ted Thibodeau (OpenLink Software Inc.),
+Curt Tilmes (National Aeronautics and Space Administration),
+Craig Trim (IBM Corporation),
+Stephan Zednik (Rensselaer Polytechnic Institute),
+Jun Zhao (University of Oxford),
+Yuting Zhao (University of Aberdeen, Computing Science).
+</p>
+ </section>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+<div style="position: absolute; visibility: hidden; top: 0px; left: 0px; width: auto; padding: 0px; border: 0px none; margin: 0px; white-space: nowrap; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; font-size: 40px; font-weight: normal; font-style: normal; font-size-adjust: none; font-family: 'STIXSizeOneSym',sans-serif;" id="MathJax_Font_Test">ˆ</div><section class="appendix" id="references"><!--OddPage--><h2><span class="secno">B. </span>References</h2><section id="informative-references"><h3><span class="secno">B.1 </span>Informative references</h3><dl class="bibliography"><dt id="bib-Logic">[Logic]</dt><dd>W. E. Johnson. <a href="http://www.ditext.com/johnson/intro-3.html"><cite>Logic: Part III</cite></a>.1924. URL: <a href="http://www.ditext.com/johnson/intro-3.html">http://www.ditext.com/johnson/intro-3.html</a>
+</dd><dt id="bib-PROV-AQ">[PROV-AQ]</dt><dd>Graham Klyne; Paul Groth; eds. <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/"><cite>Provenance Access and Query</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-aq-20130312/">http://www.w3.org/TR/2013/WD-prov-aq-20130312/</a>
+</dd><dt id="bib-PROV-CONSTRAINTS">[PROV-CONSTRAINTS]</dt><dd>James Cheney; Paolo Missier; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/"><cite>Constraints of the PROV Data Model</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-constraints-20130312/">http://www.w3.org/TR/2013/PR-prov-constraints-20130312/</a>
+</dd><dt id="bib-PROV-DC">[PROV-DC]</dt><dd>Daniel Garijo; Kai Eckert; eds. <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/"><cite>Dublin Core to PROV Mapping</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-dc-20130312/">http://www.w3.org/TR/2013/WD-prov-dc-20130312/</a>
+</dd><dt id="bib-PROV-DICTIONARY">[PROV-DICTIONARY]</dt><dd>Tom De Nies; Sam Coppens; eds. <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/"><cite>PROV Dictionary</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/">http://www.w3.org/TR/2013/WD-prov-dictionary-20130312/</a>
+</dd><dt id="bib-PROV-DM">[PROV-DM]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/"><cite>PROV-DM: The PROV Data Model</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-dm-20130312/">http://www.w3.org/TR/2013/PR-prov-dm-20130312/</a>
+</dd><dt id="bib-PROV-LINKS">[PROV-LINKS]</dt><dd>Luc Moreau; Timothy Lebo; eds. <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/"><cite>Linking Across Provenance Bundles</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-links-20130312/">http://www.w3.org/TR/2013/WD-prov-links-20130312/</a>
+</dd><dt id="bib-PROV-N">[PROV-N]</dt><dd>Luc Moreau; Paolo Missier; eds. <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/"><cite>PROV-N: The Provenance Notation</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-n-20130312/">http://www.w3.org/TR/2013/PR-prov-n-20130312/</a>
+</dd><dt id="bib-PROV-O">[PROV-O]</dt><dd>Timothy Lebo; Satya Sahoo; Deborah McGuinness; eds. <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/"><cite>PROV-O: The PROV Ontology</cite></a>. 12 March 2013, W3C Proposed Recommendation. URL: <a href="http://www.w3.org/TR/2013/PR-prov-o-20130312/">http://www.w3.org/TR/2013/PR-prov-o-20130312/</a>
+</dd><dt id="bib-PROV-OVERVIEW">[PROV-OVERVIEW]</dt><dd>Paul Groth; Luc Moreau; eds. <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/"><cite>PROV-OVERVIEW: An Overview of the PROV Family of Documents</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-overview-20130312/">http://www.w3.org/TR/2013/WD-prov-overview-20130312/</a>
+</dd><dt id="bib-PROV-PRIMER">[PROV-PRIMER]</dt><dd>Yolanda Gil; Simon Miles; eds. <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/"><cite>PROV Model Primer</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-primer-20130312/">http://www.w3.org/TR/2013/WD-prov-primer-20130312/</a>
+</dd><dt id="bib-PROV-SEM">[PROV-SEM]</dt><dd>James Cheney; ed. <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312"><cite>Semantics of the PROV Data Model</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-sem-20130312">http://www.w3.org/TR/2013/WD-prov-sem-20130312</a>.
+</dd><dt id="bib-PROV-XML">[PROV-XML]</dt><dd>Hook Hua; Curt Tilmes; Stephan Zednik; eds. <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/"><cite>PROV-XML: The PROV XML Schema</cite></a>. 12 March 2013, Working Draft. URL: <a href="http://www.w3.org/TR/2013/WD-prov-xml-20130312/">http://www.w3.org/TR/2013/WD-prov-xml-20130312/</a>
+</dd></dl></section></section></body></html>
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