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* fixed built version of semantics
authorjcheney@inf.ed.ac.uk
Mon, 25 Feb 2013 13:49:34 +0000
changeset 5734 8df8ca08c88d
parent 5733 413c06adfedb
child 5735 8c51d3082048
* fixed built version of semantics
semantics/prov-sem-review-20130226.html 
--- a/semantics/prov-sem-review-20130226.html	Mon Feb 25 13:43:46 2013 +0000
+++ b/semantics/prov-sem-review-20130226.html	Mon Feb 25 13:49:34 2013 +0000
@@ -781,7 +781,7 @@
 #MathJax_Tooltip * {filter: none; opacity: 1; background: transparent}
 @font-face {font-family: MathJax_Blank; src: url('about:blank')}
 .MathJax .noError {vertical-align: ; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid}
-</style><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></head> 
+</style><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></head> 
   <body><div style="visibility: hidden; overflow: hidden; position: absolute; top: 0px; height: 1px; width: auto; padding: 0px; border: 0px; 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 class="head">
   <p>
     
@@ -834,7 +834,7 @@
     
   
   <hr>
-</div><div id="MathJax_Message" style="">Typesetting math: 51%</div> 
+</div><div id="MathJax_Message" style="display: none;"></div> 
 
     <section id="abstract" class="introductory"><h2>Abstract</h2>
 <p>
@@ -1718,48 +1718,47 @@
 <div class="formalism" id="rule_16" data-count="16" data-title="Formalism 16 (rule_16)"><div class="ruleTitle"><a class="internalDFN" href="#rule_16">Formalism 16 (rule_16)</a></div>
   <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-237-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4745"><span style="display: inline-block; position: relative; width: 213px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4746"><span class="mi" id="MathJax-Span-4747" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4748" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4749" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-4750" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-4751" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4752" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4753" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4754" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4755" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4756" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4757" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4758" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4759" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4760" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4761" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4762" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4763" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4764" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4765" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4766" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4767" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4768" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4769" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4770" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-237">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
 
-<li>[WF] The identifier <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-238-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4771"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4772"><span class="mi" id="MathJax-Span-4773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4774" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-238">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-239-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4775"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4776"><span class="mi" id="MathJax-Span-4777" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4778" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4779" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4780" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4781" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4782" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4783" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4784" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4785" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4786" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4787" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4788" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4790" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4791" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4792" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-239">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-240-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4793"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4794"><span class="mi" id="MathJax-Span-4795" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-240">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(id) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-241-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4796"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4797"><span class="mi" id="MathJax-Span-4798" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4799" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4801" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4802" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4803" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4804" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4805" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4806" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-4809" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4811" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4812" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4813" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4814" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4815" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4816" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4817" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-241">act = \rho(id) \in Activities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-242-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4818"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4819"><span class="mi" id="MathJax-Span-4820" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-242">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-243-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4821"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4822"><span class="mi" id="MathJax-Span-4823" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4825" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4826" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4827" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4829" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4830" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4833" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4834" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4835" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4837" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4838" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4839" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-243">ent = \rho(e) \in Entities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-238-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4771"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4772"><span class="mi" id="MathJax-Span-4773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4774" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-238">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-239-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4775"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4776"><span class="mi" id="MathJax-Span-4777" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4778" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4779" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4780" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4781" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4782" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4783" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4784" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4785" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4786" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4787" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4788" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4790" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4791" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4792" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-239">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-244-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4840"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4841"><span class="mi" id="MathJax-Span-4842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4843" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-244">evt</script> is part of <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processed" id="MathJax-Element-245-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4845"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4846"><span class="mi" id="MathJax-Span-4847" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4848" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4849" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-245">act</script>, i.e. <span class="MathJax_Preview">(evt,act) \in EventActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-246-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4850"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4851"><span class="mo" id="MathJax-Span-4852" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4854" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4856" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4857" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4858" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4859" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4860" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4861" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4862" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4863" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4865" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4866" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4867" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-4868" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4869" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4870" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4871" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4872" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4873" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4874" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4875" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4876" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-246">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-247-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4877"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4878"><span class="mi" id="MathJax-Span-4879" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4880" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4881" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-247">evt</script> is <span class="MathJax_Preview">use</span><span class="MathJax MathJax_Processed" id="MathJax-Element-248-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4882"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4883"><span class="mi" id="MathJax-Span-4884" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-4885" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4886" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-248">use</script>, i.e., <span class="MathJax_Preview">type(evt) = use</span><span class="MathJax MathJax_Processed" id="MathJax-Element-249-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4887"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4888"><span class="mi" id="MathJax-Span-4889" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4890" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-4891" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-4892" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4893" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4895" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4896" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4897" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4898" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4899" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4900" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4901" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-249">type(evt) = use</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-240-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4793"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4794"><span class="mi" id="MathJax-Span-4795" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-240">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-241-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4796"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4797"><span class="mi" id="MathJax-Span-4798" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4799" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4801" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4802" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4803" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4804" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4805" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4806" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-4809" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4811" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4812" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4813" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4814" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4815" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4816" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4817" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-241">act = \rho(id) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-250-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4902"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4903"><span class="mi" id="MathJax-Span-4904" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4905" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-250">evt</script> occurred at time <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-251-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4907"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4908"><span class="mi" id="MathJax-Span-4909" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-251">t</script>, i.e. <span class="MathJax_Preview">time(evt) = t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-252-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4910"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4911"><span class="mi" id="MathJax-Span-4912" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4913" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4914" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4915" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4916" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4917" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4918" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4919" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4920" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4921" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4922" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-252">time(evt) = t</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-242-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4818"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4819"><span class="mi" id="MathJax-Span-4820" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-242">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-243-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4821"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4822"><span class="mi" id="MathJax-Span-4823" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4825" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4826" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4827" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4829" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4830" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4833" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4834" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4835" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4837" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4838" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4839" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-243">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-253-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4923"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4924"><span class="mi" id="MathJax-Span-4925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4926" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4927" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-253">evt</script> used <span class="MathJax_Preview">obj</span><span class="MathJax MathJax_Processed" id="MathJax-Element-254-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4928"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4929"><span class="mi" id="MathJax-Span-4930" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-4931" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-4932" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-254">obj</script>, i.e. <span class="MathJax_Preview">(evt,ent) \in Used</span><span class="MathJax MathJax_Processed" id="MathJax-Element-255-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4933"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4934"><span class="mo" id="MathJax-Span-4935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4936" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4937" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4939" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4940" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4941" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4942" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4943" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4944" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4945" style="font-family: STIXGeneral-Italic; padding-left: 6px;">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-4946" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4947" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4948" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-255">(evt,ent) \in Used</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-244-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4840"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4841"><span class="mi" id="MathJax-Span-4842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4843" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-244">evt</script> is part of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-245-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4845"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4846"><span class="mi" id="MathJax-Span-4847" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4848" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4849" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-245">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-246-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4850"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4851"><span class="mo" id="MathJax-Span-4852" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4854" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4856" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4857" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4858" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4859" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4860" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4861" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4862" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4863" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4865" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4866" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4867" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-4868" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4869" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4870" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4871" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4872" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4873" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4874" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4875" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4876" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-246">(evt,act) \in EventActivities</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-256-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4949"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4950"><span class="mi" id="MathJax-Span-4951" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4952" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4953" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4955" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-4956" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4957" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4958" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4959" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4960" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4961" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4962" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4963" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4965" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4966" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4967" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4968" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-256">match(W,evt,attrs)</script>.
+<li>The type of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-247-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4877"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4878"><span class="mi" id="MathJax-Span-4879" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4880" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4881" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-247">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-248-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4882"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4883"><span class="mi" id="MathJax-Span-4884" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-4885" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4886" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-248">use</script>, i.e., <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-249-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4887"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4888"><span class="mi" id="MathJax-Span-4889" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4890" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-4891" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-4892" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4893" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4895" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4896" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4897" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4898" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4899" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4900" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4901" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-249">type(evt) = use</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-250-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4902"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4903"><span class="mi" id="MathJax-Span-4904" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4905" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-250">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-251-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4907"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4908"><span class="mi" id="MathJax-Span-4909" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-251">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-252-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4910"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4911"><span class="mi" id="MathJax-Span-4912" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4913" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4914" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4915" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4916" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4917" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4918" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4919" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4920" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4921" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4922" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-252">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-253-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4923"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4924"><span class="mi" id="MathJax-Span-4925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4926" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4927" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-253">evt</script> used <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-254-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4928"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4929"><span class="mi" id="MathJax-Span-4930" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-4931" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-4932" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-254">obj</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-255-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4933"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4934"><span class="mo" id="MathJax-Span-4935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4936" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4937" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4939" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4940" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4941" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4942" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4943" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4944" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4945" style="font-family: STIXGeneral-Italic; padding-left: 6px;">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-4946" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4947" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4948" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-255">(evt,ent) \in Used</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-256-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4949"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4950"><span class="mi" id="MathJax-Span-4951" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4952" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4953" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4955" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-4956" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4957" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4958" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4959" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4960" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4961" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4962" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4963" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4965" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4966" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4967" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4968" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-256">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">wasInvalidatedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-257-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4969"><span style="display: inline-block; position: relative; width: 258px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4970"><span class="mi" id="MathJax-Span-4971" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-4972" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4973" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4974" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-4975" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4976" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4977" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4978" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-4979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4980" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4981" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4982" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4983" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4984" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4985" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-4986" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-4987" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4988" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4989" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4992" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4993" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4994" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4995" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4996" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4997" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4998" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4999" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5000" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5001" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5002" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-257">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-258-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5003"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5004"><span class="mi" id="MathJax-Span-5005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5006" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-258">id</script> is an event identifier, <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-259-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5007"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5008"><span class="mi" id="MathJax-Span-5009" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-259">e</script> is an entity identifier, <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-260-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5010"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5011"><span class="mi" id="MathJax-Span-5012" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-260">a</script> is an activity identifier, <span class="MathJax_Preview">attrs</span><span class="MathJax MathJax_Processed" id="MathJax-Element-261-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5013"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5014"><span class="mi" id="MathJax-Span-5015" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5016" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5017" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5018" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5019" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-261">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-262-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5020"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5021"><span class="mi" id="MathJax-Span-5022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-262">t</script> is an optional time.</p>
-
-<div class="formalism" id="rule_17" data-count="17" data-title="Formalism 17 (rule_17)"><div class="ruleTitle"><a class="internalDFN" href="#rule_17">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview">W,\rho \models
-  wasInvalidatedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-263-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5023"><span style="display: inline-block; position: relative; width: 317px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5024"><span class="mi" id="MathJax-Span-5025" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5026" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5027" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5028" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5029" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5030" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5032" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5033" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5034" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5036" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5037" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5038" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5039" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5041" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5042" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5043" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5044" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5045" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5046" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5047" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5048" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5049" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5050" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5051" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5052" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5053" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5054" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5055" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5056" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5057" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5058" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5059" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5060" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-263">W,\rho \models
+<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-257-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4969"><span style="display: inline-block; position: relative; width: 258px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4970"><span class="mi" id="MathJax-Span-4971" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-4972" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4973" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4974" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-4975" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4976" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4977" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4978" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-4979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4980" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4981" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4982" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4983" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4984" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4985" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-4986" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-4987" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4988" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4989" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-4990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4992" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4993" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4994" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4995" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4996" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4997" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4998" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-4999" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5000" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5001" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5002" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-257">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-258-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5003"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5004"><span class="mi" id="MathJax-Span-5005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5006" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-258">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-259-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5007"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5008"><span class="mi" id="MathJax-Span-5009" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-259">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-260-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5010"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5011"><span class="mi" id="MathJax-Span-5012" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-260">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-261-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5013"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5014"><span class="mi" id="MathJax-Span-5015" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5016" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5017" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5018" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5019" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-261">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-262-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5020"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5021"><span class="mi" id="MathJax-Span-5022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-262">t</script> is an optional time.</p>
+
+<div class="formalism" id="rule_17" data-count="17" data-title="Formalism 17 (rule_17)"><div class="ruleTitle"><a class="internalDFN" href="#rule_17">Formalism 17 (rule_17)</a></div> <p>An invaliation formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-263-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5023"><span style="display: inline-block; position: relative; width: 317px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5024"><span class="mi" id="MathJax-Span-5025" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5026" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5027" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5028" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5029" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5030" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5032" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5033" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5034" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5036" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5037" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5038" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5039" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5041" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5042" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5043" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5044" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5045" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5046" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5047" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5048" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5049" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5050" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5051" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5052" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5053" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5054" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5055" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5056" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5057" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5058" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5059" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5060" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-263">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">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-264-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5061"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5062"><span class="mi" id="MathJax-Span-5063" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5064" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-264">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-265-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5065"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5066"><span class="mi" id="MathJax-Span-5067" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5068" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5069" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5070" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5071" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5072" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5073" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5074" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5075" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5076" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5077" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5078" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5080" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5081" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5082" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-265">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-266-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5083"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5084"><span class="mi" id="MathJax-Span-5085" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-266">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-267-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5086"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5087"><span class="mi" id="MathJax-Span-5088" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5089" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5091" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5092" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5093" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5094" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5095" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5096" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5097" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5098" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5099" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5100" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5101" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5102" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5103" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5104" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-267">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-268-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5105"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5106"><span class="mi" id="MathJax-Span-5107" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-268">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-269-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5108"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5109"><span class="mi" id="MathJax-Span-5110" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5111" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5112" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5113" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5114" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5116" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5117" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5118" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5119" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5120" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5121" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5122" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5123" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5124" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5125" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5126" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5127" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5128" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-269">act = \rho(a) \in Activities</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-264-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5061"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5062"><span class="mi" id="MathJax-Span-5063" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5064" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-264">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-265-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5065"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5066"><span class="mi" id="MathJax-Span-5067" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5068" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5069" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5070" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5071" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5072" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5073" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5074" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5075" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5076" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5077" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5078" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5080" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5081" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5082" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-265">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-270-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5129"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5130"><span class="mi" id="MathJax-Span-5131" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5132" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5133" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-270">evt</script> is involved in <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processed" id="MathJax-Element-271-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5134"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5135"><span class="mi" id="MathJax-Span-5136" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5137" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5138" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-271">act</script>, that is, <span class="MathJax_Preview">(evt,act) \in EventActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-272-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5139"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5140"><span class="mo" id="MathJax-Span-5141" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5143" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5144" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5145" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5146" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5147" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5149" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5150" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5151" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5154" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5155" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5156" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5157" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5158" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5159" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5160" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5161" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5162" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5164" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5165" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-272">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-273-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5166"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5167"><span class="mi" id="MathJax-Span-5168" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5169" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-273">evt</script> is <span class="MathJax_Preview">invalidation</span><span class="MathJax MathJax_Processed" id="MathJax-Element-274-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5171"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5172"><span class="mi" id="MathJax-Span-5173" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5174" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5175" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5176" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5177" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5178" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5179" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5180" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5181" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5182" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5183" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5184" style="font-family: STIXGeneral-Italic;">n</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.6px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-274">invalidation</script>, i.e. <span class="MathJax_Preview">type(evt) = invalidation</span><span class="MathJax MathJax_Processed" id="MathJax-Element-275-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5185"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5186"><span class="mi" id="MathJax-Span-5187" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5188" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5189" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5190" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5191" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5192" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5193" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5194" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5195" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5196" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5197" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-5198" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5199" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5200" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5201" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5202" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5203" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5204" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5205" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5206" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5207" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5208" style="font-family: STIXGeneral-Italic;">n</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-275">type(evt) = invalidation</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-266-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5083"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5084"><span class="mi" id="MathJax-Span-5085" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-266">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-267-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5086"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5087"><span class="mi" id="MathJax-Span-5088" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5089" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5091" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5092" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5093" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5094" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5095" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5096" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5097" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5098" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5099" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5100" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5101" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5102" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5103" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5104" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-267">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-276-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5209"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5210"><span class="mi" id="MathJax-Span-5211" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5212" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-276">evt</script> occurred at time <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-277-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5214"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5215"><span class="mi" id="MathJax-Span-5216" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-277">t</script>, i.e. <span class="MathJax_Preview">time(evt) = t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-278-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5217"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5218"><span class="mi" id="MathJax-Span-5219" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5220" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5221" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5222" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5223" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5224" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5225" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5226" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5227" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5228" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5229" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-278">time(evt) = t</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-268-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5105"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5106"><span class="mi" id="MathJax-Span-5107" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-268">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-269-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5108"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5109"><span class="mi" id="MathJax-Span-5110" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5111" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5112" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5113" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5114" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5116" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5117" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5118" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5119" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5120" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5121" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5122" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5123" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5124" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5125" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5126" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5127" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5128" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-269">act = \rho(a) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-279-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5230"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5231"><span class="mi" id="MathJax-Span-5232" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5233" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-279">evt</script> invalidated <span class="MathJax_Preview">ent</span><span class="MathJax MathJax_Processed" id="MathJax-Element-280-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5235"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5236"><span class="mi" id="MathJax-Span-5237" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5238" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5239" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-280">ent</script>, i.e. <span class="MathJax_Preview">(evt,ent) \in Invalidated</span><span class="MathJax MathJax_Processed" id="MathJax-Element-281-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5240"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5241"><span class="mo" id="MathJax-Span-5242" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5243" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5244" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5245" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5248" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5250" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5251" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5252" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5253" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5254" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5255" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5256" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5257" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5258" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5259" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5260" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5261" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5262" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-281">(evt,ent) \in Invalidated</script>.
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-270-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5129"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5130"><span class="mi" id="MathJax-Span-5131" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5132" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5133" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-270">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-271-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5134"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5135"><span class="mi" id="MathJax-Span-5136" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5137" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5138" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-271">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-272-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5139"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5140"><span class="mo" id="MathJax-Span-5141" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5143" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5144" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5145" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5146" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5147" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5149" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5150" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5151" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5154" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5155" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5156" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5157" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5158" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5159" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5160" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5161" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5162" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5164" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5165" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-272">(evt,act) \in EventActivities</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-282-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5263"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5264"><span class="mi" id="MathJax-Span-5265" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5266" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5267" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5268" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5269" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5270" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5271" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5272" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5273" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5274" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5275" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5276" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5277" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5278" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5279" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5280" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5281" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5282" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-282">match(W,evt,attrs)</script>.
+<li>The type of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-273-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5166"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5167"><span class="mi" id="MathJax-Span-5168" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5169" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-273">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-274-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5171"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5172"><span class="mi" id="MathJax-Span-5173" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5174" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5175" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5176" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5177" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5178" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5179" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5180" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5181" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5182" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5183" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5184" style="font-family: STIXGeneral-Italic;">n</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.6px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-274">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-275-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5185"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5186"><span class="mi" id="MathJax-Span-5187" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5188" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5189" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5190" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5191" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5192" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5193" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5194" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5195" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5196" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5197" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-5198" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5199" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5200" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5201" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5202" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5203" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5204" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5205" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5206" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5207" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5208" style="font-family: STIXGeneral-Italic;">n</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-275">type(evt) = invalidation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-276-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5209"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5210"><span class="mi" id="MathJax-Span-5211" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5212" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-276">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-277-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5214"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5215"><span class="mi" id="MathJax-Span-5216" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-277">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-278-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5217"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5218"><span class="mi" id="MathJax-Span-5219" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5220" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5221" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5222" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5223" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5224" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5225" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5226" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5227" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5228" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5229" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-278">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-279-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5230"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5231"><span class="mi" id="MathJax-Span-5232" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5233" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-279">evt</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-280-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5235"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5236"><span class="mi" id="MathJax-Span-5237" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5238" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5239" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-280">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-281-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5240"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5241"><span class="mo" id="MathJax-Span-5242" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5243" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5244" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5245" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5248" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5250" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5251" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5252" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5253" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5254" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5255" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5256" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5257" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5258" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5259" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5260" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5261" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5262" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-281">(evt,ent) \in Invalidated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-282-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5263"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5264"><span class="mi" id="MathJax-Span-5265" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5266" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5267" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5268" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5269" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5270" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5271" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5272" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5273" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5274" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5275" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5276" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5277" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5278" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5279" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5280" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5281" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5282" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-282">match(W,evt,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1767,77 +1766,74 @@
 
 <h4><span class="secno">4.4.4 </span> Association </h4>
 
-<p>An association formula has the form <span class="MathJax_Preview">wasAssociatedWith(id,a,ag,pl,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-283-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5283"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5284"><span class="mi" id="MathJax-Span-5285" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5286" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5287" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5288" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5290" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5291" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5292" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5294" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5296" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5297" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5298" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5299" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5300" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5301" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5302" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5304" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5305" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5306" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5309" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5310" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5311" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5312" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5313" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5314" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5316" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5317" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5318" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5319" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-283">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
+<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-283-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5283"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5284"><span class="mi" id="MathJax-Span-5285" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5286" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5287" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5288" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5290" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5291" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5292" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5294" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5296" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5297" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5298" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5299" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5300" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5301" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5302" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5304" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5305" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5306" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5309" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5310" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5311" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5312" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5313" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5314" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5316" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5317" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5318" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5319" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-283">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
 
 <div class="formalism" id="rule_18" data-count="18" data-title="Formalism 18 (rule_18)"><div class="ruleTitle"><a class="internalDFN" href="#rule_18">Formalism 18 (rule_18)</a></div><p>
-  <span class="MathJax_Preview">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-284-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5320"><span style="display: inline-block; position: relative; width: 350px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5321"><span class="mi" id="MathJax-Span-5322" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5323" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5324" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5325" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5326" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5327" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5328" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5329" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5330" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5331" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5332" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5333" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5334" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5335" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5336" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5337" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5338" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5339" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5340" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5341" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5342" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5343" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5344" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5345" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5346" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5347" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5348" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5349" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5350" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5351" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5352" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5354" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5355" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5356" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5357" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5358" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5359" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5360" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-284">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-284-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5320"><span style="display: inline-block; position: relative; width: 350px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5321"><span class="mi" id="MathJax-Span-5322" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5323" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5324" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5325" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5326" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5327" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5328" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5329" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5330" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5331" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5332" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5333" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5334" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5335" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5336" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5337" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5338" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5339" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5340" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5341" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5342" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5343" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5344" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5345" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5346" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5347" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5348" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5349" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5350" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5351" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5352" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5354" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5355" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5356" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5357" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5358" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5359" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5360" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-284">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">assoc</span><span class="MathJax MathJax_Processed" id="MathJax-Element-285-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5361"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5362"><span class="mi" id="MathJax-Span-5363" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5364" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5365" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5366" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5367" style="font-family: STIXGeneral-Italic;">c</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-285">assoc</script> denotes an association <span class="MathJax_Preview">assoc = \rho(id) \in Associations</span><span class="MathJax MathJax_Processed" id="MathJax-Element-286-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5368"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5369"><span class="mi" id="MathJax-Span-5370" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5371" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5372" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5373" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5374" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5375" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5376" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5377" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5378" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5379" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5380" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5381" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5382" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5383" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5384" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5385" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5386" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5387" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5388" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5389" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5390" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5391" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5392" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5393" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-286">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-287-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5394"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5395"><span class="mi" id="MathJax-Span-5396" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-287">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-288-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5397"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5398"><span class="mi" id="MathJax-Span-5399" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5400" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5401" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5402" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5403" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5404" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5405" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5406" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5407" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5408" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5409" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5410" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5411" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5412" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5413" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5414" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5415" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5416" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5417" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-288">act = \rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-285-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5361"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5362"><span class="mi" id="MathJax-Span-5363" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5364" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5365" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5366" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5367" style="font-family: STIXGeneral-Italic;">c</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-285">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-286-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5368"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5369"><span class="mi" id="MathJax-Span-5370" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5371" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5372" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5373" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5374" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5375" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5376" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5377" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5378" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5379" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5380" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5381" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5382" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5383" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5384" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5385" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5386" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5387" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5388" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5389" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5390" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5391" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5392" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5393" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-286">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag</span><span class="MathJax MathJax_Processed" id="MathJax-Element-289-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5418"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5419"><span class="mi" id="MathJax-Span-5420" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5421" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-289">ag</script> denotes an agent <span class="MathJax_Preview">agent = \rho(ag) \in Agents</span><span class="MathJax MathJax_Processed" id="MathJax-Element-290-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5422"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5423"><span class="mi" id="MathJax-Span-5424" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5425" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5426" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5427" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5429" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5430" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5431" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5432" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5433" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5437" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5438" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5439" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5441" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-290">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-287-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5394"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5395"><span class="mi" id="MathJax-Span-5396" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-287">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-288-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5397"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5398"><span class="mi" id="MathJax-Span-5399" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5400" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5401" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5402" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5403" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5404" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5405" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5406" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5407" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5408" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5409" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5410" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5411" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5412" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5413" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5414" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5415" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5416" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5417" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-288">act = \rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">pl</span><span class="MathJax MathJax_Processed" id="MathJax-Element-291-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5442"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5443"><span class="mi" id="MathJax-Span-5444" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5445" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-291">pl</script> is either the placeholder <span class="MathJax_Preview">-</span><span class="MathJax MathJax_Processed" id="MathJax-Element-292-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5446"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5447"><span class="mo" id="MathJax-Span-5448" style="font-family: STIXGeneral-Regular;">−</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-292">-</script> or denotes a plan <span class="MathJax_Preview">plan=\rho(pl) \in Plans</span><span class="MathJax MathJax_Processed" id="MathJax-Element-293-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5449"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5450"><span class="mi" id="MathJax-Span-5451" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5452" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5453" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5454" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5455" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5456" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5457" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5458" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5459" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5460" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5461" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5462" style="font-family: STIXGeneral-Italic; padding-left: 6px;">P</span><span class="mi" id="MathJax-Span-5463" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5464" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5465" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5466" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-293">plan=\rho(pl) \in Plans</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-289-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5418"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5419"><span class="mi" id="MathJax-Span-5420" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5421" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-289">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-290-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5422"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5423"><span class="mi" id="MathJax-Span-5424" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5425" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5426" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5427" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5429" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5430" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5431" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5432" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5433" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5437" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5438" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5439" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5441" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-290">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview">(assoc,agent,act,plan) \in AssociatedWith</span><span class="MathJax MathJax_Processed" id="MathJax-Element-294-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5467"><span style="display: inline-block; position: relative; width: 324px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5468"><span class="mo" id="MathJax-Span-5469" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5470" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5471" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5472" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5473" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5474" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5475" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5476" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5477" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5478" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5479" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5480" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5483" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5485" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5486" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5487" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5488" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5489" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5490" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5491" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5492" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5493" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5494" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5495" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5496" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5497" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5498" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5499" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5501" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5502" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5504" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5505" style="font-family: STIXGeneral-Italic;">h</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-294">(assoc,agent,act,plan) \in AssociatedWith</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-291-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5442"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5443"><span class="mi" id="MathJax-Span-5444" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5445" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-291">pl</script> is either the placeholder <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-292-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5446"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5447"><span class="mo" id="MathJax-Span-5448" style="font-family: STIXGeneral-Regular;">−</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-292">-</script> or denotes a plan <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-293-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5449"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5450"><span class="mi" id="MathJax-Span-5451" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5452" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5453" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5454" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5455" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5456" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5457" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5458" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5459" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5460" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5461" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5462" style="font-family: STIXGeneral-Italic; padding-left: 6px;">P</span><span class="mi" id="MathJax-Span-5463" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5464" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5465" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5466" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-293">plan=\rho(pl) \in Plans</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,assoc,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-295-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5506"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5507"><span class="mi" id="MathJax-Span-5508" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5509" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5510" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5511" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5512" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5513" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5514" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5515" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5516" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5517" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5518" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5519" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5520" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5521" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5522" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5523" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5524" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5525" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5526" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5527" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-295">match(W,assoc,attrs)</script>.
+<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-294-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5467"><span style="display: inline-block; position: relative; width: 324px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5468"><span class="mo" id="MathJax-Span-5469" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5470" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5471" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5472" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5473" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5474" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5475" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5476" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5477" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5478" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5479" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5480" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5483" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5485" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5486" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5487" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5488" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5489" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5490" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5491" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5492" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5493" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5494" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5495" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5496" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5497" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5498" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5499" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5501" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5502" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5504" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5505" style="font-family: STIXGeneral-Italic;">h</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-294">(assoc,agent,act,plan) \in AssociatedWith</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-295-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5506"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5507"><span class="mi" id="MathJax-Span-5508" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5509" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5510" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5511" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5512" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5513" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5514" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5515" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5516" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5517" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5518" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5519" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5520" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5521" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5522" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5523" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5524" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5525" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5526" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5527" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-295">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">wasStartedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-296-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5528"><span style="display: inline-block; position: relative; width: 247px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5529"><span class="mi" id="MathJax-Span-5530" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5531" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5532" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5533" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5534" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5535" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5536" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5537" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5538" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5539" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5540" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5541" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5542" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5543" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5544" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5545" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5546" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5547" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5548" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5549" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5550" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5551" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5552" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5553" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5554" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5555" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5556" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5557" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5558" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5559" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5560" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5561" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-296">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-296-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5528"><span style="display: inline-block; position: relative; width: 247px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5529"><span class="mi" id="MathJax-Span-5530" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5531" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5532" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5533" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5534" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5535" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5536" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5537" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5538" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5539" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5540" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5541" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5542" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5543" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5544" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5545" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5546" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5547" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5548" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5549" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5550" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5551" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5552" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5553" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5554" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5555" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5556" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5557" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5558" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5559" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5560" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5561" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-296">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
 
 <div class="formalism" id="rule_19" data-count="19" data-title="Formalism 19 (rule_19)"><div class="ruleTitle"><a class="internalDFN" href="#rule_19">Formalism 19 (rule_19)</a></div>
-  <p><span class="MathJax_Preview">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-297-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5562"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5563"><span class="mi" id="MathJax-Span-5564" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5565" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5566" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5567" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5568" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5569" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5570" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5571" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5572" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5573" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5574" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5575" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5576" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5577" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5578" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5579" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5580" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5581" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5582" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5583" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5584" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5585" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5586" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5587" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5588" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5589" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5590" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5591" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5592" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5593" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5594" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5595" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5596" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5597" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5598" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5599" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-297">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-297-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5562"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5563"><span class="mi" id="MathJax-Span-5564" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5565" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5566" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5567" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5568" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5569" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5570" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5571" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5572" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5573" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5574" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5575" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5576" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5577" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5578" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5579" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5580" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5581" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5582" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5583" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5584" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5585" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5586" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5587" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5588" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5589" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5590" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5591" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5592" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5593" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5594" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5595" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5596" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5597" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5598" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5599" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-297">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">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-298-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5600"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5601"><span class="mi" id="MathJax-Span-5602" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5603" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-298">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-299-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5604"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5605"><span class="mi" id="MathJax-Span-5606" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5607" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5609" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5610" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5611" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5612" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5613" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5614" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5615" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5616" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5617" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5618" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5619" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5620" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5621" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-299">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">a_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-300-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5622"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5623"><span class="msubsup" id="MathJax-Span-5624"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5625" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5626" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-300">a_2</script> denotes an activity <span class="MathJax_Preview">act_2 = \rho(a_2) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-301-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5627"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5628"><span class="mi" id="MathJax-Span-5629" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5630" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5631"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5632" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5633" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5634" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5635" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5636" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5637"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5638" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5639" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5640" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5641" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5642" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5643" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5644" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5645" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5646" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5647" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5648" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5649" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5651" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-301">act_2 = \rho(a_2) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-302-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5652"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5653"><span class="mi" id="MathJax-Span-5654" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-302">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-303-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5655"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5656"><span class="mi" id="MathJax-Span-5657" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5658" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5660" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5661" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5662" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5663" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5664" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5665" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5666" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5667" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5668" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5669" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5670" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5672" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5673" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-303">ent = \rho(e) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-298-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5600"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5601"><span class="mi" id="MathJax-Span-5602" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5603" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-298">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-299-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5604"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5605"><span class="mi" id="MathJax-Span-5606" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5607" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5609" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5610" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5611" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5612" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5613" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5614" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5615" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5616" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5617" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5618" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5619" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5620" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5621" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-299">evt = \rho(id) \in Events</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-304-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5674"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5675"><span class="msubsup" id="MathJax-Span-5676"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5677" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5678" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-304">a_1</script> denotes an activity <span class="MathJax_Preview">act_1 = \rho(a_1) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-305-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5679"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5680"><span class="mi" id="MathJax-Span-5681" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5682" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5683"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5684" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5685" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5686" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5687" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5688" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5689"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5690" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5691" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5692" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5693" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5694" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5695" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5696" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5697" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5698" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5699" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5700" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5701" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5702" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5703" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-305">act_1 = \rho(a_1) \in Activities</script>.
-</li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-306-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5704"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5705"><span class="mi" id="MathJax-Span-5706" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5707" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-306">evt</script> has type <span class="MathJax_Preview">start</span><span class="MathJax MathJax_Processed" id="MathJax-Element-307-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5709"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5710"><span class="mi" id="MathJax-Span-5711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5712" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5713" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5714" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5715" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-307">start</script>, i.e. <span class="MathJax_Preview">type(evt) = start</span><span class="MathJax MathJax_Processed" id="MathJax-Element-308-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5716"><span style="display: inline-block; position: relative; width: 125px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5717"><span class="mi" id="MathJax-Span-5718" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5719" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5720" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5721" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5722" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5723" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5724" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5725" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5726" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5727" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5728" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-5729" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5730" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5731" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5732" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-308">type(evt) = start</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-300-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5622"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5623"><span class="msubsup" id="MathJax-Span-5624"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5625" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5626" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-300">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-301-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5627"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5628"><span class="mi" id="MathJax-Span-5629" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5630" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5631"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5632" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5633" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5634" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5635" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5636" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5637"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5638" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5639" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5640" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5641" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5642" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5643" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5644" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5645" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5646" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5647" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5648" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5649" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5651" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-301">act_2 = \rho(a_2) \in Activities</script>.
 </li>
-<li>The event happened at the start of <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-309-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5733"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5734"><span class="mi" id="MathJax-Span-5735" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5736" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5737"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5738" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5739" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-309">act_2</script>, that is, <span class="MathJax_Preview">(evt,act_2)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-310-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5740"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5741"><span class="mo" id="MathJax-Span-5742" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5743" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5744" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5748" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5749"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5750" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5751" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5752" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5753" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5754" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5755" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5757" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5758" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5759" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5760" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5761" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5762" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5764" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5765" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5766" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5767" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5769" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-310">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview">min(lifetime(act_2)) = time(evt)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-311-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5770"><span style="display: inline-block; position: relative; width: 234px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5771"><span class="mi" id="MathJax-Span-5772" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5774" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5775" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5776" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5777" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5778" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-5779" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5780" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5781" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5782" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5783" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5784" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5785" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5786" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5787"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5788" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5789" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5790" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5791" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5792" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5793" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5795" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5796" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5797" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5798" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5799" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5801" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-311">min(lifetime(act_2)) = time(evt)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-302-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5652"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5653"><span class="mi" id="MathJax-Span-5654" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-302">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-303-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5655"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5656"><span class="mi" id="MathJax-Span-5657" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5658" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5660" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5661" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5662" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5663" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5664" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5665" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5666" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5667" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5668" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5669" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5670" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5672" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5673" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-303">ent = \rho(e) \in Entities</script>.
 </li>
-<li>TODO: The entity <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-312-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5802"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5803"><span class="mi" id="MathJax-Span-5804" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-312">e</script> was generated by <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-313-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5805"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5806"><span class="mi" id="MathJax-Span-5807" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5808" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5809"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5811" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-313">act_1</script> and started <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-314-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5812"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5813"><span class="mi" id="MathJax-Span-5814" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5815" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5816"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5817" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5818" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-314">act_2</script>.
-</li><li>The event happened during <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-315-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5819"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5820"><span class="mi" id="MathJax-Span-5821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5822" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5823"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5824" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5825" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-315">act_1</script>, that is, <span class="MathJax_Preview">(evt,act_1)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-316-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5826"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5827"><span class="mo" id="MathJax-Span-5828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5829" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5830" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5832" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5833" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5834" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5835"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5837" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5838" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5839" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5840" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5843" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5845" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5846" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5847" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5848" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5849" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5850" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5851" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5852" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5853" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5854" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5855" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-316">(evt,act_1)
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-304-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5674"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5675"><span class="msubsup" id="MathJax-Span-5676"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5677" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5678" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-304">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-305-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5679"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5680"><span class="mi" id="MathJax-Span-5681" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5682" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5683"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5684" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5685" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5686" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5687" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5688" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5689"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5690" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5691" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5692" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5693" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5694" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5695" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5696" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5697" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5698" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5699" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5700" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5701" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5702" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5703" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-305">act_1 = \rho(a_1) \in Activities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-306-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5704"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5705"><span class="mi" id="MathJax-Span-5706" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5707" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-306">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-307-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5709"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5710"><span class="mi" id="MathJax-Span-5711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5712" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5713" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5714" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5715" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-307">start</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-308-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5716"><span style="display: inline-block; position: relative; width: 125px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5717"><span class="mi" id="MathJax-Span-5718" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5719" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5720" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5721" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5722" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5723" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5724" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5725" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5726" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5727" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5728" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-5729" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5730" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5731" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5732" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-308">type(evt) = start</script>.
+</li>
+<li>The event happened at the start of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-309-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5733"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5734"><span class="mi" id="MathJax-Span-5735" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5736" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5737"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5738" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5739" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-309">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-310-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5740"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5741"><span class="mo" id="MathJax-Span-5742" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5743" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5744" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5748" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5749"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5750" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5751" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5752" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5753" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5754" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5755" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5757" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5758" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5759" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5760" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5761" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5762" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5764" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5765" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5766" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5767" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5769" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-310">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-311-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5770"><span style="display: inline-block; position: relative; width: 234px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5771"><span class="mi" id="MathJax-Span-5772" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5774" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5775" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5776" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5777" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5778" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-5779" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5780" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5781" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5782" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5783" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5784" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5785" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5786" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5787"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5788" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5789" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5790" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5791" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5792" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5793" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5795" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5796" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5797" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5798" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5799" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5801" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-311">min(lifetime(act_2)) = time(evt)</script>.
+</li>
+<li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-312-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5802"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5803"><span class="mi" id="MathJax-Span-5804" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-312">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-313-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5805"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5806"><span class="mi" id="MathJax-Span-5807" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5808" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5809"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5811" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-313">act_1</script> and started <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-314-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5812"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5813"><span class="mi" id="MathJax-Span-5814" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5815" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5816"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5817" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5818" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-314">act_2</script>.
+</li><li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-315-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5819"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5820"><span class="mi" id="MathJax-Span-5821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5822" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5823"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5824" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5825" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-315">act_1</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-316-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5826"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5827"><span class="mo" id="MathJax-Span-5828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5829" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5830" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5832" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5833" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5834" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5835"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5837" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5838" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5839" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5840" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5843" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5845" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5846" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5847" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5848" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5849" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5850" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5851" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5852" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5853" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5854" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5855" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-316">(evt,act_1)
   \in EventsActivities</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-317-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5856"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5857"><span class="mi" id="MathJax-Span-5858" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5860" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5861" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5862" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5863" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5864" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5865" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5866" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5867" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5869" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5870" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5871" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5872" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5873" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5874" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5875" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-317">match(W,evt,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-317-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5856"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5857"><span class="mi" id="MathJax-Span-5858" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5860" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5861" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5862" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5863" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5864" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5865" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5866" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5867" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5869" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5870" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5871" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5872" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5873" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5874" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5875" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-317">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">wasEndedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-318-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5876"><span style="display: inline-block; position: relative; width: 241px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5877"><span class="mi" id="MathJax-Span-5878" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5879" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5880" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5881" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5883" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5884" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5885" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5886" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5887" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5888" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5889" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5890" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5891" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5892" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5893" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5894" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5895" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5896" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5897" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5898" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5899" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5900" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5903" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5904" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5905" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5906" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5907" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-318">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-318-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5876"><span style="display: inline-block; position: relative; width: 241px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5877"><span class="mi" id="MathJax-Span-5878" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5879" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5880" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5881" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5883" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5884" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5885" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5886" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5887" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5888" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5889" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5890" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5891" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5892" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5893" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5894" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5895" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5896" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5897" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5898" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5899" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5900" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5903" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5904" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5905" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5906" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5907" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-318">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
 
 <div class="formalism" id="rule_20" data-count="20" data-title="Formalism 20 (rule_20)"><div class="ruleTitle"><a class="internalDFN" href="#rule_20">Formalism 20 (rule_20)</a></div>
 <p>
-  <span class="MathJax_Preview">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-319-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5908"><span style="display: inline-block; position: relative; width: 301px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5909"><span class="mi" id="MathJax-Span-5910" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5913" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5914" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5915" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5916" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5917" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5918" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5919" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5920" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5921" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5922" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5923" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5924" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5925" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5926" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5927" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5928" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5929" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5930" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5931" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5932" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5933" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5934" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5935" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5936" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5937" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5938" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5939" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5940" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5941" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5942" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5943" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-319">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</script> holds if and only
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-319-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5908"><span style="display: inline-block; position: relative; width: 301px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5909"><span class="mi" id="MathJax-Span-5910" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5913" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5914" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5915" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5916" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5917" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5918" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5919" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5920" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5921" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5922" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5923" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5924" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5925" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5926" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5927" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5928" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5929" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5930" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5931" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5932" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5933" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5934" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5935" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5936" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5937" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5938" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5939" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5940" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5941" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5942" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5943" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-319">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">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-320-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5944"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5945"><span class="mi" id="MathJax-Span-5946" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5947" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-320">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-321-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5948"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5949"><span class="mi" id="MathJax-Span-5950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5951" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5953" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5954" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5955" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5956" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5957" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5958" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5959" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5960" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5961" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5962" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5963" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5965" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-321">evt = \rho(id) \in Events</script>.</li>
-<li> [WF] <span class="MathJax_Preview">a_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-322-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5966"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5967"><span class="msubsup" id="MathJax-Span-5968"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5969" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5970" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-322">a_2</script> denotes an activity <span class="MathJax_Preview">act_2 = \rho(a_2)\in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-323-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5971"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5972"><span class="mi" id="MathJax-Span-5973" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5974" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5975"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5976" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5977" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5978" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5979" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5980" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5981"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5982" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5983" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5984" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5985" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5986" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5987" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5988" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5989" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5990" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5991" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5992" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5993" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5995" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-323">act_2 = \rho(a_2)\in Activities</script>.</li>
-<li> [WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-324-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5996"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5997"><span class="mi" id="MathJax-Span-5998" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-324">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e)\in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-325-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5999"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6000"><span class="mi" id="MathJax-Span-6001" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6002" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6003" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6004" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6005" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6006" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6007" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6008" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6009" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6010" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6011" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6012" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6013" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6014" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6015" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6016" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6017" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-325">ent = \rho(e)\in Entities</script>.</li>
-<li>[WF] <span class="MathJax_Preview">a_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-326-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6018"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-6019"><span class="msubsup" id="MathJax-Span-6020"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6021" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-6022" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-326">a_1</script> denotes an activity <span class="MathJax_Preview">act_1 = \rho(a_1)\in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-327-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6023"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6024"><span class="mi" id="MathJax-Span-6025" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6026" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6027"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6028" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6029" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6030" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6031" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6032" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6033"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6034" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-6035" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6036" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6037" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6038" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6039" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6041" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6042" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6044" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6045" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6046" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6047" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-327">act_1 = \rho(a_1)\in Activities</script>.</li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-328-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6048"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6049"><span class="mi" id="MathJax-Span-6050" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6051" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-328">evt</script> has type <span class="MathJax_Preview">end</span><span class="MathJax MathJax_Processed" id="MathJax-Element-329-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6053"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6054"><span class="mi" id="MathJax-Span-6055" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6056" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6057" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-329">end</script>, i.e. <span class="MathJax_Preview">type(evt) = end</span><span class="MathJax MathJax_Processed" id="MathJax-Element-330-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6058"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6059"><span class="mi" id="MathJax-Span-6060" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6061" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6062" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6063" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6064" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6065" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6066" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6068" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6069" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6070" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6071" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6072" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-330">type(evt) = end</script>.</li>
-<li>The event happened at the end of <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-331-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6073"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6074"><span class="mi" id="MathJax-Span-6075" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6076" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6077"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6078" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6079" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-331">act_2</script>, that is, <span class="MathJax_Preview">(evt,act_2)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-332-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6080"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6081"><span class="mo" id="MathJax-Span-6082" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6083" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6084" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6085" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6086" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6087" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6088" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6089"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6091" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6092" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6093" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6094" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6095" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6096" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6097" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6098" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6099" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6100" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6101" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6102" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6103" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6104" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6105" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6107" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6108" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6109" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-332">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview">max(lifetime(act_2)) = time(evt)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-333-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6110"><span style="display: inline-block; position: relative; width: 237px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6111"><span class="mi" id="MathJax-Span-6112" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6113" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6114" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-6115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6116" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6117" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6118" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6119" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6120" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6122" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6123" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6124" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6125" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6126" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6127"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6128" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6129" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6130" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6131" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6132" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6133" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6134" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6135" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6136" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6137" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6138" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6139" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6140" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6141" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-333">max(lifetime(act_2)) = time(evt)</script>.</li>
-  <li>TODO: The entity <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-334-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6142"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6143"><span class="mi" id="MathJax-Span-6144" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-334">e</script> was generated by <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-335-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6145"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6146"><span class="mi" id="MathJax-Span-6147" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6148" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6149"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6150" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6151" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-335">act_1</script> and ended <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-336-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6152"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6153"><span class="mi" id="MathJax-Span-6154" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6155" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6156"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6157" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6158" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-336">act_2</script>.</li>
-
-<li>The event happened during <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-337-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6159"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6160"><span class="mi" id="MathJax-Span-6161" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6162" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6163"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6164" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6165" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-337">act_1</script>, that is, $(evt,act_1) \in EventActivities.</li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-338-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6166"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6167"><span class="mi" id="MathJax-Span-6168" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6169" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6171" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6172" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6173" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6174" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6175" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6176" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6177" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6178" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6179" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6180" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6181" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6182" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6183" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6184" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6185" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-338">match(W,evt,attrs)</script>.</li>
+  <li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-320-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5944"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5945"><span class="mi" id="MathJax-Span-5946" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5947" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-320">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-321-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5948"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5949"><span class="mi" id="MathJax-Span-5950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5951" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5953" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5954" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5955" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5956" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5957" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-5958" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5959" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5960" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5961" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5962" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5963" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5965" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-321">evt = \rho(id) \in Events</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-322-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5966"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5967"><span class="msubsup" id="MathJax-Span-5968"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5969" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5970" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-322">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-323-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5971"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5972"><span class="mi" id="MathJax-Span-5973" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5974" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5975"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5976" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-5977" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5978" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5979" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5980" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5981"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-5982" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-5983" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-5984" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5985" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5986" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5987" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5988" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5989" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5990" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5991" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5992" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5993" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5995" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-323">act_2 = \rho(a_2)\in Activities</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-324-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5996"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5997"><span class="mi" id="MathJax-Span-5998" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-324">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-325-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5999"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6000"><span class="mi" id="MathJax-Span-6001" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6002" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6003" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6004" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6005" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6006" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6007" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6008" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6009" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6010" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6011" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6012" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6013" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6014" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6015" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6016" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6017" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-325">ent = \rho(e)\in Entities</script>.</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-326-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6018"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-6019"><span class="msubsup" id="MathJax-Span-6020"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6021" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-6022" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-326">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-327-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6023"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6024"><span class="mi" id="MathJax-Span-6025" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6026" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6027"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6028" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6029" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6030" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6031" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6032" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6033"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6034" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-6035" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6036" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6037" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6038" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6039" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6041" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6042" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6044" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6045" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6046" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6047" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-327">act_1 = \rho(a_1)\in Activities</script>.</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-328-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6048"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6049"><span class="mi" id="MathJax-Span-6050" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6051" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-328">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-329-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6053"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6054"><span class="mi" id="MathJax-Span-6055" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6056" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6057" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-329">end</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-330-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6058"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6059"><span class="mi" id="MathJax-Span-6060" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6061" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6062" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6063" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6064" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6065" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6066" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6068" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6069" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6070" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6071" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6072" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-330">type(evt) = end</script>.</li>
+<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-331-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6073"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6074"><span class="mi" id="MathJax-Span-6075" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6076" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6077"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6078" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6079" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-331">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-332-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6080"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6081"><span class="mo" id="MathJax-Span-6082" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6083" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6084" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6085" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6086" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6087" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6088" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6089"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6091" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6092" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6093" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6094" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6095" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6096" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6097" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6098" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6099" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6100" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6101" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6102" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6103" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6104" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6105" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6107" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6108" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6109" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-332">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-333-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6110"><span style="display: inline-block; position: relative; width: 237px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6111"><span class="mi" id="MathJax-Span-6112" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6113" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6114" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-6115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6116" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6117" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6118" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6119" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6120" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6122" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6123" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6124" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6125" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6126" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6127"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6128" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6129" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6130" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6131" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6132" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6133" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6134" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6135" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6136" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6137" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6138" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6139" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6140" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6141" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-333">max(lifetime(act_2)) = time(evt)</script>.</li>
+  <li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-334-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6142"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6143"><span class="mi" id="MathJax-Span-6144" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-334">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-335-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6145"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6146"><span class="mi" id="MathJax-Span-6147" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6148" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6149"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6150" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6151" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-335">act_1</script> and ended <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-336-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6152"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6153"><span class="mi" id="MathJax-Span-6154" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6155" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6156"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6157" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6158" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-336">act_2</script>.</li>
+
+<li>The event happened during <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-337-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6159"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6160"><span class="mi" id="MathJax-Span-6161" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6162" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6163"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6164" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6165" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-337">act_1</script>, that is, $(evt,act_1) \in EventActivities.</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-338-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6166"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6167"><span class="mi" id="MathJax-Span-6168" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6169" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6171" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6172" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6173" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6174" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6175" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6176" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6177" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6178" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6179" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6180" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6181" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6182" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6183" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6184" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6185" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-338">match(W,evt,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1846,23 +1842,23 @@
 <h4><span class="secno">4.4.7 </span> Attribution </h4>
 
 <p>
-An attribution formula <span class="MathJax_Preview">wasAttributedTo(id,e,ag,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-339-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6186"><span style="display: inline-block; position: relative; width: 246px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6187"><span class="mi" id="MathJax-Span-6188" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6189" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6190" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6191" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6192" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6193" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6194" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6195" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6196" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6197" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6198" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6199" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6200" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6201" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6202" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6203" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6204" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6205" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6206" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6207" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6208" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6209" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6210" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6211" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6212" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6214" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6215" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6216" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6217" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-339">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
+An attribution formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-339-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6186"><span style="display: inline-block; position: relative; width: 246px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6187"><span class="mi" id="MathJax-Span-6188" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6189" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6190" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6191" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6192" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6193" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6194" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6195" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6196" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6197" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6198" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6199" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6200" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6201" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6202" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6203" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6204" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6205" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6206" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6207" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6208" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6209" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6210" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6211" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6212" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6214" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6215" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6216" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6217" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-339">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
 </p>
 <div class="formalism" id="rule_21" data-count="21" data-title="Formalism 21 (rule_21)"><div class="ruleTitle"><a class="internalDFN" href="#rule_21">Formalism 21 (rule_21)</a></div>
   <p>
-  <span class="MathJax_Preview">W,\rho \models wasAttributedTo(id,e,ag,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-340-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6218"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6219"><span class="mi" id="MathJax-Span-6220" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6221" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6222" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6223" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6224" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6226" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6227" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6228" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6229" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6230" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6231" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6232" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6233" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6235" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6236" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6237" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6238" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6239" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6240" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6241" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6242" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6243" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6244" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6245" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6246" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6247" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6248" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6250" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6251" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6252" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6253" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-340">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-340-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6218"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6219"><span class="mi" id="MathJax-Span-6220" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6221" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6222" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6223" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6224" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6226" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6227" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6228" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6229" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6230" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6231" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6232" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6233" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6235" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6236" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6237" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6238" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6239" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6240" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6241" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6242" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6243" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6244" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6245" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6246" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6247" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6248" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6250" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6251" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6252" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6253" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-340">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
   holds if and only if:
   </p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-341-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-341">id</script> denotes an association <span class="MathJax_Preview">assoc = \rho(id) \in Associations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-342-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-342">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processing" id="MathJax-Element-343-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-343">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-344-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-344">ent = \rho(e) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-341-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6254"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6255"><span class="mi" id="MathJax-Span-6256" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6257" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-341">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-342-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6258"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6259"><span class="mi" id="MathJax-Span-6260" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6261" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6262" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6263" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6264" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6265" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6266" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6267" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6268" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6269" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6270" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6271" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6272" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6273" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6274" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6275" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6276" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6277" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6278" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6279" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6280" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6281" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6282" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6283" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-342">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag</span><span class="MathJax MathJax_Processing" id="MathJax-Element-345-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-345">ag</script> denotes an agent <span class="MathJax_Preview">agent = \rho(ag) \in Agents</span><span class="MathJax MathJax_Processing" id="MathJax-Element-346-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-346">agent = \rho(ag) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-343-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6284"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6285"><span class="mi" id="MathJax-Span-6286" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-343">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-344-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6287"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6288"><span class="mi" id="MathJax-Span-6289" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6290" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6291" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6292" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6293" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6294" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6295" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6296" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6297" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6298" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6299" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6300" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6301" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6302" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6304" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6305" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-344">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview">(assoc,ent,agent) \in AttributedTo</span><span class="MathJax MathJax_Processing" id="MathJax-Element-347-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-347">(assoc,ent,agent) \in AttributedTo</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-345-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6306"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6307"><span class="mi" id="MathJax-Span-6308" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6309" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-345">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-346-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6310"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6311"><span class="mi" id="MathJax-Span-6312" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6313" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6314" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6315" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6316" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6317" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6318" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6319" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6320" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6321" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6322" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6323" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6324" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6325" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6326" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6327" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6328" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6329" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-346">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-348-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-348">match(W,evt,attrs)</script>.
+<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-347-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6330"><span style="display: inline-block; position: relative; width: 261px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6331"><span class="mo" id="MathJax-Span-6332" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6333" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6334" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6335" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6336" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6337" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6338" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6339" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6340" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6341" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6342" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6343" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6344" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6345" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6346" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6347" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6348" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6349" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6350" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6351" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6352" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6353" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6354" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6355" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6356" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6357" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6358" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6359" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6360" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6361" style="font-family: STIXGeneral-Italic;">o</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-347">(assoc,ent,agent) \in AttributedTo</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-348-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6362"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6363"><span class="mi" id="MathJax-Span-6364" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6365" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6366" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6367" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6368" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6369" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6370" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6371" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6372" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6373" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6374" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6375" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6376" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6377" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6378" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6379" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6380" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6381" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-348">match(W,evt,attrs)</script>.
 </li></ol>
 </div>
 </section>
@@ -1878,21 +1874,21 @@
 
 <h4><span class="secno">4.4.9 </span> Responsibility </h4>
 
-<p>The <span class="MathJax_Preview">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-349-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-349">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview">ActsFor</span><span class="MathJax MathJax_Processing" id="MathJax-Element-350-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-350">ActsFor</script> relation as follows:</p>
+<p>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-349-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6382"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6383"><span class="mi" id="MathJax-Span-6384" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6385" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6386" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6387" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6388" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6389" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6390" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6391" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-6392" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6393" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-6394" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6395" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6396" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6397" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6398" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-6399" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6400" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6401" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6402" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6403" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6404"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6405" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6406" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6407" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6408" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6409"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6410" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6411" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6412" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6413" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6414" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6415" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6416" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6417" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6418" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6419" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6420" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6421" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6422" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-349">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> relation is interpreted using the <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-350-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6423"><span style="display: inline-block; position: relative; width: 63px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.1px 19360px 51.3px -10px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6424"><span class="mi" id="MathJax-Span-6425" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6426" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6427" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6428" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6429" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6430" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6431" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-350">ActsFor</script> relation as follows:</p>
 
 <div class="formalism" id="rule_22" data-count="22" data-title="Formalism 22 (rule_22)"><div class="ruleTitle"><a class="internalDFN" href="#rule_22">Formalism 22 (rule_22)</a></div>
   <p>
-  <span class="MathJax_Preview">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-351-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-351">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-351-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6432"><span style="display: inline-block; position: relative; width: 375px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6433"><span class="mi" id="MathJax-Span-6434" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6435" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6436" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6437" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6438" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-6439" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6441" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6442" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6443" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6444" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6445" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-6446" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6447" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-6448" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6449" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6450" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6451" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6452" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-6453" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6454" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6455" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6456" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6457" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6458"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6459" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6460" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6461" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6462" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6463"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6464" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6465" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6466" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6467" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6468" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6469" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6470" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6471" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6472" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6473" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6474" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6475" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6476" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-351">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">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-352-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-352">id</script> denotes an association <span class="MathJax_Preview">deleg=\rho(id) \in Delegations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-353-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-353">deleg=\rho(id) \in Delegations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-352-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6477"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6478"><span class="mi" id="MathJax-Span-6479" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6480" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-352">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-353-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6481"><span style="display: inline-block; position: relative; width: 220px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6482"><span class="mi" id="MathJax-Span-6483" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6484" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6485" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6486" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6487" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6488" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6489" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6490" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6491" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6492" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6493" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6494" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6495" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-6496" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6497" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6498" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6499" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6500" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6501" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6502" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6503" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6504" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6505" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-353">deleg=\rho(id) \in Delegations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-354-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-354">a</script> denotes an activity <span class="MathJax_Preview">act=\rho(a) \in Activities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-355-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-355">act=\rho(a) \in Activities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-354-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6506"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6507"><span class="mi" id="MathJax-Span-6508" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-354">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-355-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6509"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6510"><span class="mi" id="MathJax-Span-6511" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6512" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6513" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6514" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6515" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6516" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6517" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-6518" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6519" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6520" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6521" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6522" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6523" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6524" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6525" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6526" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6527" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6528" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6529" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-355">act=\rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag_1,ag_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-356-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-356">ag_1,ag_2</script> denote agents <span class="MathJax_Preview">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</span><span class="MathJax MathJax_Processing" id="MathJax-Element-357-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-357">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-356-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6530"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6531"><span class="mi" id="MathJax-Span-6532" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6533"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6534" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6535" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6536" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6537" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6538"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6539" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6540" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-356">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-357-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6541"><span style="display: inline-block; position: relative; width: 339px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6542"><span class="mi" id="MathJax-Span-6543" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6544" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6545" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6546" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6547"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6548" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6549" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6550" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6551" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6552" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6553" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6554"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6555" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6556" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6557" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6558" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6559" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6560" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6561" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6562" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6563"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6564" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6565" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6566" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6567" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6568" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6569" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6570"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6571" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6572" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6573" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6574" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6575" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6576" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6577" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6578" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6579" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6580" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.8px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-357">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
 </li>
-<li>The agent <span class="MathJax_Preview">agent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-358-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-358">agent_2</script> acts for the agent <span class="MathJax_Preview">agent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-359-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-359">agent_1</script> with respect to the activity <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processing" id="MathJax-Element-360-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-360">act</script>, i.e. <span class="MathJax_Preview">(deleg,agent_2,agent_1,act) \in ActsFor</span><span class="MathJax MathJax_Processing" id="MathJax-Element-361-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-361">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
+<li>The agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-358-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6581"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6582"><span class="mi" id="MathJax-Span-6583" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6584" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6585" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6586" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6587"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6588" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6589" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 16.6px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-358">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-359-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6590"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6591"><span class="mi" id="MathJax-Span-6592" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6593" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6594" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6595" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6596"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6597" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6598" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 16.6px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-359">agent_1</script> with respect to the activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-360-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6599"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6600"><span class="mi" id="MathJax-Span-6601" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6602" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6603" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-360">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-361-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6604"><span style="display: inline-block; position: relative; width: 291px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6605"><span class="mo" id="MathJax-Span-6606" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6607" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6608" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6609" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6610" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6611" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6612" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6613" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6614" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6615" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6616" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6617"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6618" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6619" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6620" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6621" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6622" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6623" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6624" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6625"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6626" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6627" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6628" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6629" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6630" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6631" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6632" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6633" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6634" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6635" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6636" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6637" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6638" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6639" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6640" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-361">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,assoc,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-362-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-362">match(W,assoc,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-362-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6641"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6642"><span class="mi" id="MathJax-Span-6643" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6644" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6645" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6646" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6647" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6648" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6649" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6650" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6651" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6652" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6653" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6654" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6655" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6656" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6657" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6658" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6660" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6661" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6662" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-362">match(W,assoc,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1904,26 +1900,25 @@
 <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">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-363-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-363">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
+<p>A precise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-363-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6663"><span style="display: inline-block; position: relative; width: 309px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6664"><span class="mi" id="MathJax-Span-6665" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6666" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6667" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6668" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6669" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6670" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6672" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6673" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6674" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6675" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6676" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6677" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6678" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6679" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6680" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6681" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6682" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6683" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6684" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6685" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6686" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6687" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6688" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6689" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6690" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6691" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-6692" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6693" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-6694" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6695" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-6696" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6697" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6698" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6699" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6700" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6701" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6702" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-363">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</script>.
 </p>
 <div class="formalism" id="rule_23" data-count="23" data-title="Formalism 23 (rule_23)"><div class="ruleTitle"><a class="internalDFN" href="#rule_23">Formalism 23 (rule_23)</a></div>
-  <p><span class="MathJax_Preview">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-364-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-364">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</script> holds if and only if:</p>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-364-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6703"><span style="display: inline-block; position: relative; width: 382px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6704"><span class="mi" id="MathJax-Span-6705" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6706" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6707" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6708" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6709" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6710" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6712" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6713" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6714" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6715" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6716" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6717" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6718" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6719" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6720" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6721" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6722" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6723" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6724" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6725" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6726" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6727" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6728" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6729" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6730" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6731" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6732" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6733" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6734" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6735" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6736" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6737" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6738" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6739" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-6740" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6741" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-6742" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6743" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6744" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6746" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6747" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6748" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-364">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">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-365-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-365">id</script> denotes a derivation <span class="MathJax_Preview">deriv = \rho(id) \in Derivations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-366-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-366">deriv = \rho(id) \in Derivations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e_1,e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-367-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-367">e_1,e_2</script> denote entities <span class="MathJax_Preview">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-368-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-368">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> .
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-365-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6749"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6750"><span class="mi" id="MathJax-Span-6751" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6752" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-365">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-366-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6753"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6754"><span class="mi" id="MathJax-Span-6755" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6757" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6758" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6759" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6760" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6761" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6762" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6764" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-6765" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6766" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6767" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-6768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6769" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6770" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6771" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6772" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6773" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6774" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6775" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6776" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6777" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-366">deriv = \rho(id) \in Derivations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-369-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-369">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-370-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-370">act = \rho(a) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">g</span><span class="MathJax MathJax_Processing" id="MathJax-Element-371-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-371">g</script> denotes a generation event <span class="MathJax_Preview">gen = \rho(g) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-372-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-372">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview">type(\rho(g)) = generation</span><span class="MathJax MathJax_Processing" id="MathJax-Element-373-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-373">type(\rho(g)) = generation</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-367-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6778"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6779"><span class="msubsup" id="MathJax-Span-6780"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6781" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6782" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6783" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6784" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6785" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6786" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-367">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-368-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6787"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6788"><span class="mi" id="MathJax-Span-6789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6790" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6791"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6792" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6793" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6794" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6795" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6796" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6797"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6798" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6799" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6800" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6801" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6802" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6803" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6804"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6805" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6806" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6809" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6810"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6811" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6812" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6813" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6814" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6815" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6816" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6817" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6818" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6819" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6820" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6821" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6822" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-368">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> .
 </li>
-<li>[WF] <span class="MathJax_Preview">u</span><span class="MathJax MathJax_Processing" id="MathJax-Element-374-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-374">u</script> denotes a use event <span class="MathJax_Preview">\rho(u) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-375-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-375">\rho(u) \in Events</script> and <span class="MathJax_Preview">type(\rho(u)) = use</span><span class="MathJax MathJax_Processing" id="MathJax-Element-376-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-376">type(\rho(u)) = use</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-369-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6823"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6824"><span class="mi" id="MathJax-Span-6825" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-369">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-370-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6826"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6827"><span class="mi" id="MathJax-Span-6828" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6829" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6830" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6833" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6834" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-6835" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6836" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6837" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6838" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6839" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6840" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6842" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6843" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6844" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6845" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6846" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-370">act = \rho(a) \in Activities</script>.
 </li>
-<li>The derivation denotes a one-step derivation <span class="MathJax_Preview">derivedFrom(deriv) =
-ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-377-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-377">derivedFrom(deriv) =
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-371-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6847"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6848"><span class="mi" id="MathJax-Span-6849" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-371">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-372-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6850"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6851"><span class="mi" id="MathJax-Span-6852" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6854" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-6855" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6856" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6857" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6858" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6859" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6860" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6861" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6862" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6863" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6864" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6865" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6866" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-372">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-373-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6867"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6868"><span class="mi" id="MathJax-Span-6869" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6870" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6871" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6872" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6873" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6874" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6875" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6876" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6877" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6878" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6879" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6880" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-6881" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6883" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6884" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6885" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6886" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6887" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6888" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6889" style="font-family: STIXGeneral-Italic;">n</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-373">type(\rho(g)) = generation</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-374-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6890"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6891"><span class="mi" id="MathJax-Span-6892" style="font-family: STIXGeneral-Italic;">u</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-374">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-375-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6893"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6894"><span class="mi" id="MathJax-Span-6895" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6896" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6897" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-6898" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6899" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6900" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6901" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6902" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6903" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6904" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6905" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-375">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-376-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6906"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6907"><span class="mi" id="MathJax-Span-6908" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6909" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6910" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6911" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6912" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6913" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6914" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6915" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-6916" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6917" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6918" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6919" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-6920" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6921" style="font-family: STIXGeneral-Italic;">e</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-376">type(\rho(u)) = use</script>.
+</li>
+<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-377-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6922"><span style="display: inline-block; position: relative; width: 382px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6923"><span class="mi" id="MathJax-Span-6924" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6926" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6927" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6928" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6929" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6930" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6931" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6932" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6933" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6934" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6936" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6937" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6938" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6939" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6940" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6941" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6942" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6943" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6944" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6945"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6946" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6947" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-6948" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6949" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">g</span><span class="mi" id="MathJax-Span-6950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6951" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-6952" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6953" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">a</span><span class="mi" id="MathJax-Span-6954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6955" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6956" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6957" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-6958" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6959" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6960" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6961" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">e</span><span class="mi" id="MathJax-Span-6962" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6963"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-6965" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-377">derivedFrom(deriv) =
 ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,deriv,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-378-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-378">match(W,deriv,attrs)</script>.</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-378-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6966"><span style="display: inline-block; position: relative; width: 167px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6967"><span class="mi" id="MathJax-Span-6968" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6969" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6970" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6971" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6972" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6973" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6974" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6975" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6976" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6977" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6978" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6980" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6981" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6982" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6983" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6984" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6985" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6986" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6987" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-378">match(W,deriv,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1931,18 +1926,18 @@
 
 <h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
 <p>
-An imprecise derivation formula has the form <span class="MathJax_Preview">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-379-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-379">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
+An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-379-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6988"><span style="display: inline-block; position: relative; width: 318px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6989"><span class="mi" id="MathJax-Span-6990" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6991" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6992" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6993" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6995" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6996" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6997" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6998" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6999" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7000" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7001" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7002" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7003" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7004" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7006" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-7007" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7008" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7009" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7010" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7011" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7012" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7013" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7014" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7015" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7016" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7017" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7018" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7019" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7020" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7021" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7022" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7023" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7024" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7025" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7026" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7027" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-379">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
 
 <div class="formalism" id="rule_24" data-count="24" data-title="Formalism 24 (rule_24)"><div class="ruleTitle"><a class="internalDFN" href="#rule_24">Formalism 24 (rule_24)</a></div>
-  <p><span class="MathJax_Preview">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-380-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-380">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-380-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7028"><span style="display: inline-block; position: relative; width: 377px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7029"><span class="mi" id="MathJax-Span-7030" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7031" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7032" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7033" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7034" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-7035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7036" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-7037" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-7038" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7039" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7040" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7041" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7042" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7043" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7044" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7045" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7046" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7047" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7048" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7049" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7050" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-7051" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7052" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7053" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7054" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7055" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7056" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7057" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7058" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7059" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7060" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7061" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7062" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7063" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7064" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7065" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7066" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7068" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7069" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7070" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7071" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-380">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-381-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-381">id</script> denotes a derivation <span class="MathJax_Preview">deriv = \rho(id) \in Derivations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-382-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-382">deriv = \rho(id) \in Derivations</script>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-381-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7072"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7073"><span class="mi" id="MathJax-Span-7074" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7075" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-381">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-382-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7076"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7077"><span class="mi" id="MathJax-Span-7078" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7080" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7081" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7082" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7083" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7084" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7085" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7086" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7087" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-7088" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7089" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7090" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-7091" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7092" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7093" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7094" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7095" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7096" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7097" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7098" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7099" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7100" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-382">deriv = \rho(id) \in Derivations</script>
 </li>
-<li>[WF] <span class="MathJax_Preview">e_1,e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-383-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-383">e_1,e_2</script> denote entities <span class="MathJax_Preview">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-384-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-384">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> 
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-383-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7101"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7102"><span class="msubsup" id="MathJax-Span-7103"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7104" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7105" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7106" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7107" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7108" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7109" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-383">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-384-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7110"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7111"><span class="mi" id="MathJax-Span-7112" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7113" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7114"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7115" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7116" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7117" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7118" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7119" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7120"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7121" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7122" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7123" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7124" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7125" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-7126" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7127"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7128" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7129" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7130" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7131" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7132" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7133"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7134" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7135" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7136" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7137" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7138" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7139" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7140" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7141" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7142" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7143" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7144" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7145" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-384">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> 
 </li>
-<li><span class="MathJax_Preview">derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-385-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-385">derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1</script> for some <span class="MathJax_Preview">w</span><span class="MathJax MathJax_Processing" id="MathJax-Element-386-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-386">w</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-385-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7146"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7147"><span class="mi" id="MathJax-Span-7148" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7149" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7150" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7151" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7154" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7155" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7156" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7157" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7158" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7159" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7160" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7161" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7162" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7164" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7165" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7166" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7167" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-7168" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7169"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7171" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7172" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-7173" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mo" id="MathJax-Span-7174" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-7175" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">e</span><span class="mi" id="MathJax-Span-7176" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7177"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7178" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7179" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-385">derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1</script> for some <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-386-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7180"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7181"><span class="mi" id="MathJax-Span-7182" style="font-family: STIXGeneral-Italic;">w</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-386">w</script>
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,deriv,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-387-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-387">match(W,deriv,attrs)</script>.
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-387-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7183"><span style="display: inline-block; position: relative; width: 167px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7184"><span class="mi" id="MathJax-Span-7185" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7186" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7187" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7188" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7189" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-7190" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7191" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7192" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7193" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7194" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7195" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7196" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7197" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7198" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7199" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7200" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7201" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7202" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7203" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7204" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-387">match(W,deriv,attrs)</script>.
 </li></ol></div>
 </section>
 </section>
@@ -1957,7 +1952,7 @@
 <section id="specialization">
 <h4><span class="secno">4.4.12 </span> Specialization </h4>
 
-<p>The <span class="MathJax_Preview">specializationOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-388-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-388">specializationOf(e_1,e_2)</script> relation indicates when one entity formula presents more specific aspects of another.  
+<p>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-388-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7205"><span style="display: inline-block; position: relative; width: 181px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7206"><span class="mi" id="MathJax-Span-7207" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-7208" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7209" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7210" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7211" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7212" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7213" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7214" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7215" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-7216" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7217" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7218" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7219" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7220" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7221" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7222" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7223" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7224"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7225" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7226" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7227" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7228" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7229" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7230" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7231" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-388">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
@@ -1966,26 +1961,25 @@
     </div></div>
     
 <div class="formalism" id="rule_25" data-count="25" data-title="Formalism 25 (rule_25)"><div class="ruleTitle"><a class="internalDFN" href="#rule_25">Formalism 25 (rule_25)</a></div>  <p>
-  <span class="MathJax_Preview">W,\rho \models specializationOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-389-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-389">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-389-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7232"><span style="display: inline-block; position: relative; width: 240px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7233"><span class="mi" id="MathJax-Span-7234" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7235" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7236" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7237" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7238" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-7239" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7240" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7241" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7242" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7243" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7244" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7245" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7246" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-7247" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7248" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7249" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7250" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7251" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7252" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7253" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7254" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7255"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7256" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7257" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7258" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7259" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7260" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7261" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7262" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-389">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview">e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-390-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-390">e_1</script> and <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-391-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-391">e_2</script> are entity identifiers, denoting
-  distinct entities <span class="MathJax_Preview">ent_1
-  = \rho(e_1) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-392-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-392">ent_1
-  = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-393-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-393">ent_2 = \rho(e_2) \in Entities</script>,
-  where <span class="MathJax_Preview">ent_1 \neq ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-394-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-394">ent_1 \neq ent_2</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-390-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7263"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7264"><span class="msubsup" id="MathJax-Span-7265"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7266" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7267" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-390">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-391-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7268"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7269"><span class="msubsup" id="MathJax-Span-7270"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7271" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7272" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-391">e_2</script> are entity identifiers, denoting
+  distinct entities <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-392-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7273"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7274"><span class="mi" id="MathJax-Span-7275" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7276" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7277"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7278" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7279" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7280" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7281" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7282" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7283"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7284" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7285" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7286" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7287" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7288" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7289" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7290" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7291" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7292" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7294" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7295" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-392">ent_1
+  = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-393-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7296"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7297"><span class="mi" id="MathJax-Span-7298" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7299" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7300"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7301" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7302" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7303" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7304" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7305" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7306"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7307" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7308" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7309" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7310" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7311" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7312" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7313" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7314" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7316" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7317" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7318" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-393">ent_2 = \rho(e_2) \in Entities</script>,
+  where <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-394-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7319"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 54px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7320"><span class="mi" id="MathJax-Span-7321" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7322" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7323"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7324" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7325" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7326" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≠</span><span class="mi" id="MathJax-Span-7327" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-7328" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7329"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7330" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7331" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.8px; vertical-align: -4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-394">ent_1 \neq ent_2</script>.
 </li>
-<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview">thingOf(ent_1) = thingOf(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-395-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-395">thingOf(ent_1) = thingOf(ent_2)</script>.
+<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-395-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7332"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7333"><span class="mi" id="MathJax-Span-7334" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7335" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7336" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7337" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7338" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7339" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7340" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7341" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7342" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7343" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7344"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7345" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7346" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7347" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7348" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7349" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7350" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7351" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7352" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7353" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7354" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7355" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7356" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7357" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7358" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7359"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7360" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7361" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7362" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-395">thingOf(ent_1) = thingOf(ent_2)</script>.
 </li>
-<li>The lifetime of <span class="MathJax_Preview">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-396-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-396">obj_1</script> is contained in that of <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-397-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-397">ent_2</script>, i.e. <span class="MathJax_Preview">lifetime(ent_1) \subseteq lifetime(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-398-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-398">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-396-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7363"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7364"><span class="mi" id="MathJax-Span-7365" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7366" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7367"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7368" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7369" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-396">obj_1</script> is contained in that of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-397-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7370"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7371"><span class="mi" id="MathJax-Span-7372" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7373" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7374"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7375" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7376" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-397">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-398-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7377"><span style="display: inline-block; position: relative; width: 230px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7378"><span class="mi" id="MathJax-Span-7379" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7380" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7381" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-7382" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7383" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7384" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7385" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7386" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7387" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7388" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7389" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7390"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7391" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7392" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7393" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7394" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊆</span><span class="mi" id="MathJax-Span-7395" style="font-family: STIXGeneral-Italic; padding-left: 6px;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7396" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7397" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-7398" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7399" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7400" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7401" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7402" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7403" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7404" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7405" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7406"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7407" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7408" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7409" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-398">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
 </li>
-<li>For each attribute <span class="MathJax_Preview">attr</span><span class="MathJax MathJax_Processing" id="MathJax-Element-399-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-399">attr</script> we have <span class="MathJax_Preview">value(obj_1,attr) \supseteq value(obj_2,attr)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-400-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-400">value(obj_1,attr) \supseteq value(obj_2,attr)</script>.
+<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-399-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7410"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7411"><span class="mi" id="MathJax-Span-7412" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7413" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7414" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7415" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-399">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-400-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7416"><span style="display: inline-block; position: relative; width: 270px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7417"><span class="mi" id="MathJax-Span-7418" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7419" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7420" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7421" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7422" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7423" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7424" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7425" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7426"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7427" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7428" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7429" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7430" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7431" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7432" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7433" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-7436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-7437" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7438" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7439" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7440" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7441" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7442" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7443" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7444"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7445" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7446" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7447" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7448" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7449" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7450" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7451" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7452" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-400">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">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-401-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-401">obj_1</script> and
-<span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-402-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-402">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-403-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-403">obj_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-404-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-404">obj_1</script> to have more defined attributes than
-<span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-405-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-405">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-406-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-406">obj_2</script>.
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-401-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7453"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7454"><span class="mi" id="MathJax-Span-7455" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7456" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7457"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7458" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7459" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-401">obj_1</script> and
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-402-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7460"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7461"><span class="mi" id="MathJax-Span-7462" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7463" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7464"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7465" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7466" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-402">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-403-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7467"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7468"><span class="mi" id="MathJax-Span-7469" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7470" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7471"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7472" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7473" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-403">obj_2</script> can be larger).
+The last criterion allows <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-404-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7474"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7475"><span class="mi" id="MathJax-Span-7476" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7477" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7478"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7479" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7480" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-404">obj_1</script> to have more defined attributes than
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-405-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7481"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7482"><span class="mi" id="MathJax-Span-7483" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7484" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7485"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7486" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7487" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-405">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-406-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7488"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7489"><span class="mi" id="MathJax-Span-7490" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7491" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7492"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7493" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7494" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-406">obj_2</script>.
 </p>
 
 </section>
@@ -1993,15 +1987,15 @@
 
 <h4><span class="secno">4.4.13 </span> Alternate </h4>
 
-<p>The <span class="MathJax_Preview">alternateOf</span><span class="MathJax MathJax_Processing" id="MathJax-Element-407-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-407">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>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-407-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7495"><span style="display: inline-block; position: relative; width: 91px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7496"><span class="mi" id="MathJax-Span-7497" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7498" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7499" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7501" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7502" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7503" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7504" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7505" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7506" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7507" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-407">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 class="formalism" id="rule_26" data-count="26" data-title="Formalism 26 (rule_26)"><div class="ruleTitle"><a class="internalDFN" href="#rule_26">Formalism 26 (rule_26)</a></div>
   <p>
-  <span class="MathJax_Preview">W,\rho \models alternateOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-408-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-408">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-408-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7508"><span style="display: inline-block; position: relative; width: 204px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7509"><span class="mi" id="MathJax-Span-7510" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7511" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7512" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7513" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7514" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-7515" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7516" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7517" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7518" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7519" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7520" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7521" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7522" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7523" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7524" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7525" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7526"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7527" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7528" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7529" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7530" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7531" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7532" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7533" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-408">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview">e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-409-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-409">e_1</script> and <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-410-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-410">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview">ent_1 = \rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-411-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-411">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-412-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-412">ent_2 = \rho(e_2)</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-409-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7534"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7535"><span class="msubsup" id="MathJax-Span-7536"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7537" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7538" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-409">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-410-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7539"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7540"><span class="msubsup" id="MathJax-Span-7541"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7542" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7543" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-410">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-411-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7544"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7545"><span class="mi" id="MathJax-Span-7546" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7547" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7548"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7549" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7550" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7551" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7552" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7553" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7554"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7555" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7556" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7557" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-411">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-412-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7558"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7559"><span class="mi" id="MathJax-Span-7560" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7561" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7562"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7563" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7564" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7565" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7566" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7567" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7568"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7569" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7570" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7571" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-412">ent_2 = \rho(e_2)</script>.
 </li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview">thingOf(ent_1) = thingOf(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-413-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-413">thingOf(ent_1) = thingOf(ent_2)</script>
+<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-413-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7572"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7573"><span class="mi" id="MathJax-Span-7574" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7575" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7576" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7577" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7578" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7579" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7580" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7581" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7582" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7583" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7584"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7585" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7586" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7587" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7588" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7589" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7590" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7591" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7592" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7593" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7594" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7595" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7596" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7597" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7598" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7599"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7600" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-7601" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-7602" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-413">thingOf(ent_1) = thingOf(ent_2)</script>
 </li></ol>
 </div>
 
@@ -2013,15 +2007,14 @@
 
 <h4><span class="secno">4.4.14 </span> Membership </h4>
 
-<p>The <span class="MathJax_Preview">hadMember</span><span class="MathJax MathJax_Processing" id="MathJax-Element-414-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-414">hadMember</script> relation relates a collection to an element of the collection.
+<p>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-414-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7603"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7604"><span class="mi" id="MathJax-Span-7605" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7606" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7607" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7608" style="font-family: STIXGeneral-Italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-7609" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7610" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7611" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-7612" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7613" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-414">hadMember</script> relation relates a collection to an element of the collection.
 </p>
 <div class="formalism" id="rule_27" data-count="27" data-title="Formalism 27 (rule_27)"><div class="ruleTitle"><a class="internalDFN" href="#rule_27">Formalism 27 (rule_27)</a></div>
   <p>
-  <span class="MathJax_Preview">W,\rho \models hadMember(c,e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-415-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-415">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-415-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7614"><span style="display: inline-block; position: relative; width: 191px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7615"><span class="mi" id="MathJax-Span-7616" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7617" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7618" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7619" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7620" style="font-family: STIXGeneral-Italic; padding-left: 6px;">h</span><span class="mi" id="MathJax-Span-7621" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7622" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7623" style="font-family: STIXGeneral-Italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-7624" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7625" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7626" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-7627" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7628" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7629" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7630" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-7631" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7632" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-7633" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-415">W,\rho \models hadMember(c,e)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview">e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-416-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-416">e_1</script> and <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-417-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-417">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview">coll
-  = \rho(c) \in Collections</span><span class="MathJax MathJax_Processing" id="MathJax-Element-418-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-418">coll
-  = \rho(c) \in Collections</script> and <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-419-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-419">ent = \rho(e) \in Entities</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-416-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7634"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7635"><span class="msubsup" id="MathJax-Span-7636"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7637" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7638" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-416">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-417-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7639"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7640"><span class="msubsup" id="MathJax-Span-7641"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7642" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7643" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-417">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-418-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7644"><span style="display: inline-block; position: relative; width: 193px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7645"><span class="mi" id="MathJax-Span-7646" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7647" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7648" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7649" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-7650" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7651" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7652" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7653" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-7654" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7655" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7656" style="font-family: STIXGeneral-Italic; padding-left: 6px;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7657" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7658" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7659" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7660" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7661" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7662" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7663" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7664" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7665" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7666" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-418">coll
+  = \rho(c) \in Collections</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-419-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7667"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7668"><span class="mi" id="MathJax-Span-7669" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7670" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7671" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-7672" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7673" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7674" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7675" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7676" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7677" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7678" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7679" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7680" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7681" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7682" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7683" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7684" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7685" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-419">ent = \rho(e) \in Entities</script>.
 </li>
 <li>TODO
 </li></ol>
@@ -2046,41 +2039,38 @@
   <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">Objects</span><span class="MathJax MathJax_Processing" id="MathJax-Element-420-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-420">Objects</script>.</p>
+  the same value.  Identifiers always denote <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-420-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7686"><span style="display: inline-block; position: relative; width: 58px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7687"><span class="mi" id="MathJax-Span-7688" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7689" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-7690" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7691" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7692" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7693" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7694" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-420">Objects</script>.</p>
   <div class="formalism" id="equality" data-count="28" data-title="Formalism 28 (equality)"><div class="ruleTitle"><a class="internalDFN" href="#equality">Formalism 28 (equality)</a></div>
-    <p><span class="MathJax_Preview">W,\rho \models x = y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-421-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-421">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview">\rho(x) =
-    \rho(y)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-422-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-422">\rho(x) =
+    <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-421-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7695"><span style="display: inline-block; position: relative; width: 101px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7696"><span class="mi" id="MathJax-Span-7697" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7698" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7699" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7700" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7701" style="font-family: STIXGeneral-Italic; padding-left: 6px;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7702" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7703" style="font-family: STIXGeneral-Italic; padding-left: 6px;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.8px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-421">W,\rho \models x = y</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-422-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7704"><span style="display: inline-block; position: relative; width: 86px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7705"><span class="mi" id="MathJax-Span-7706" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7707" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7708" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7709" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7710" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7711" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7712" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7713" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7714" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-422">\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">x \preceq y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-423-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-423">x \preceq y</script> holds between two events, one taking
+  <p>The precedes relation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-423-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7715"><span style="display: inline-block; position: relative; width: 40px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(33.2px 19360px 55px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7716"><span class="mi" id="MathJax-Span-7717" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7718" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-7719" style="font-family: STIXGeneral-Italic; padding-left: 6px;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.8px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-423">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">x
-  \prec y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-424-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-424">x
-  \prec y</script> is similar, only <span class="MathJax_Preview">x</span><span class="MathJax MathJax_Processing" id="MathJax-Element-425-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-425">x</script> must take place strictly before <span class="MathJax_Preview">y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-426-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-426">y</script>).</p>
+  comparing the event times.  The semantics of strictly precedes (<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-424-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7720"><span style="display: inline-block; position: relative; width: 40px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.7px 19360px 55px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7721"><span class="mi" id="MathJax-Span-7722" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7723" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≺</span><span class="mi" id="MathJax-Span-7724" style="font-family: STIXGeneral-Italic; padding-left: 6px;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 16.3px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-424">x
+  \prec y</script> is similar, only <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-425-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7725"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7726"><span class="mi" id="MathJax-Span-7727" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-425">x</script> must take place strictly before <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-426-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7728"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7729"><span class="mi" id="MathJax-Span-7730" style="font-family: STIXGeneral-Italic;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-426">y</script>).</p>
   <div class="formalism" id="precedes" data-count="29" data-title="Formalism 29 (precedes)"><div class="ruleTitle"><a class="internalDFN" href="#precedes">Formalism 29 (precedes)</a></div>
     <ol>
-      <li><span class="MathJax_Preview">W,\rho \models x \preceq y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-427-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-427">W,\rho \models x \preceq y</script> holds if and only if
-      <span class="MathJax_Preview">\rho(x),\rho(y) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-428-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-428">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview">time(\rho(x)) \leq time(\rho(y))</span><span class="MathJax MathJax_Processing" id="MathJax-Element-429-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-429">time(\rho(x)) \leq time(\rho(y))</script>.</li>
-      <li><span class="MathJax_Preview">W,\rho \models x \prec y</span><span class="MathJax MathJax_Processing" id="MathJax-Element-430-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-430">W,\rho \models x \prec y</script> holds if and only if
-       <span class="MathJax_Preview">\rho(x),\rho(y) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-431-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-431">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview">time(\rho(x)) &lt; time(\rho(y))</span><span class="MathJax MathJax_Processing" id="MathJax-Element-432-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-432">time(\rho(x)) < time(\rho(y))</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-427-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7731"><span style="display: inline-block; position: relative; width: 99px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7732"><span class="mi" id="MathJax-Span-7733" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7734" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7735" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7736" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7737" style="font-family: STIXGeneral-Italic; padding-left: 6px;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7738" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-7739" style="font-family: STIXGeneral-Italic; padding-left: 6px;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.8px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-427">W,\rho \models x \preceq y</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-428-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7740"><span style="display: inline-block; position: relative; width: 142px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7741"><span class="mi" id="MathJax-Span-7742" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7743" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7744" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7745" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7748" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7749" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7750" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7751" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7752" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7753" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7754" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7755" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7756" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7757" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-428">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-429-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7758"><span style="display: inline-block; position: relative; width: 176px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7759"><span class="mi" id="MathJax-Span-7760" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7761" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7762" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7763" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7764" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7765" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7766" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7767" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7768" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7769" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7770" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≤</span><span class="mi" id="MathJax-Span-7771" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7772" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7773" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7774" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7775" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7776" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7777" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7778" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7779" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7780" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-429">time(\rho(x)) \leq time(\rho(y))</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-430-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7781"><span style="display: inline-block; position: relative; width: 99px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7782"><span class="mi" id="MathJax-Span-7783" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7784" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7785" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7786" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7787" style="font-family: STIXGeneral-Italic; padding-left: 6px;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7788" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≺</span><span class="mi" id="MathJax-Span-7789" style="font-family: STIXGeneral-Italic; padding-left: 6px;">y</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.8px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-430">W,\rho \models x \prec y</script> holds if and only if
+       <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-431-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7790"><span style="display: inline-block; position: relative; width: 142px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7791"><span class="mi" id="MathJax-Span-7792" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7793" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7794" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7795" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7796" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7797" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7798" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7799" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7800" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7801" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7802" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7803" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7804" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7805" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7806" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7807" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-431">\rho(x),\rho(y) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-432-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7808"><span style="display: inline-block; position: relative; width: 174px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7809"><span class="mi" id="MathJax-Span-7810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7811" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7812" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7813" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7814" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7815" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7816" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7817" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7818" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7819" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7820" style="font-family: STIXGeneral-Regular; padding-left: 6px;">&lt;</span><span class="mi" id="MathJax-Span-7821" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7822" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7823" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7824" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7825" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7826" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7827" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7828" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7829" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7830" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-432">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">notNull(x)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-433-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-433">notNull(x)</script> formula is used to specify that a value may not
-  be the null value <span class="MathJax_Preview">\bot</span><span class="MathJax MathJax_Processing" id="MathJax-Element-434-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-434">\bot</script>.  The symbol <span class="MathJax_Preview">-</span><span class="MathJax MathJax_Processing" id="MathJax-Element-435-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-435">-</script> always denotes the null
-  value (i.e. <span class="MathJax_Preview">\rho(-) = \bot</span><span class="MathJax MathJax_Processing" id="MathJax-Element-436-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-436">\rho(-) = \bot</script>).
+  <p>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-433-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7831"><span style="display: inline-block; position: relative; width: 80px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7832"><span class="mi" id="MathJax-Span-7833" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7834" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7835" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7836" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-7837" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7838" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7839" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-7840" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7841" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7842" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-433">notNull(x)</script> formula is used to specify that a value may not
+  be the null value <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-434-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7843"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7844"><span class="mi" id="MathJax-Span-7845" style="font-family: STIXGeneral-Regular;">⊥</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.8px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-434">\bot</script>.  The symbol <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-435-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7846"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7847"><span class="mo" id="MathJax-Span-7848" style="font-family: STIXGeneral-Regular;">−</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-435">-</script> always denotes the null
+  value (i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-436-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7849"><span style="display: inline-block; position: relative; width: 74px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7850"><span class="mi" id="MathJax-Span-7851" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7852" style="font-family: STIXGeneral-Regular;">(</span><span class="mo" id="MathJax-Span-7853" style="font-family: STIXGeneral-Regular;">−</span><span class="mo" id="MathJax-Span-7854" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7855" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7856" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊥</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-436">\rho(-) = \bot</script>).
   </p><div class="formalism" id="notNull" data-count="30" data-title="Formalism 30 (notNull)"><div class="ruleTitle"><a class="internalDFN" href="#notNull">Formalism 30 (notNull)</a></div>
-    <p><span class="MathJax_Preview">W,\rho\models notNull(e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-437-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-437">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview">e \neq
-  \bot</span><span class="MathJax MathJax_Processing" id="MathJax-Element-438-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-438">e \neq
+    <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-437-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7857"><span style="display: inline-block; position: relative; width: 139px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7858"><span class="mi" id="MathJax-Span-7859" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7860" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7861" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7862" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7863" style="font-family: STIXGeneral-Italic; padding-left: 6px;">n</span><span class="mi" id="MathJax-Span-7864" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7865" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7866" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-7867" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7868" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7869" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-7870" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7871" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7872" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-437">W,\rho\models notNull(e)</script> holds if and only if <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-438-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7873"><span style="display: inline-block; position: relative; width: 50px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 54px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7874"><span class="mi" id="MathJax-Span-7875" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7876" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≠</span><span class="mi" id="MathJax-Span-7877" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊥</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.8px; vertical-align: -4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-438">e \neq
   \bot</script>.
       </p>
   </div> 
@@ -2090,19 +2080,19 @@
   <section id="typeof">
   <h4><span class="secno">4.5.4 </span>typeOf</h4>
   
-  <p>The typing formula <span class="MathJax_Preview">typeOf(x,t)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-439-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-439">typeOf(x,t)</script> constrains the type of the value of
-  <span class="MathJax_Preview">x</span><span class="MathJax MathJax_Processing" id="MathJax-Element-440-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-440">x</script>.  </p>
+  <p>The typing formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-439-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7878"><span style="display: inline-block; position: relative; width: 87px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7879"><span class="mi" id="MathJax-Span-7880" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7881" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-7882" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7883" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7884" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7885" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7886" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7887" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span><span class="mo" id="MathJax-Span-7888" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7889" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-7890" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-439">typeOf(x,t)</script> constrains the type of the value of
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-440-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7891"><span style="display: inline-block; position: relative; width: 9px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -9.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7892"><span class="mi" id="MathJax-Span-7893" style="font-family: STIXGeneral-Italic;">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-440">x</script>.  </p>
 
   <div class="formalism" id="typeOf" data-count="31" data-title="Formalism 31 (typeOf)"><div class="ruleTitle"><a class="internalDFN" href="#typeOf">Formalism 31 (typeOf)</a></div>
-    <ol><li><span class="MathJax_Preview">W,\rho\models typeOf(e,entity)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-441-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-441">W,\rho\models typeOf(e,entity)</script> holds if and only if
-      <span class="MathJax_Preview">\rho(e) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-442-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-442">\rho(e) \in Entities</script>.</li>
-      <li><span class="MathJax_Preview">W,\rho\models typeOf(a,activity)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-443-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-443">W,\rho\models typeOf(a,activity)</script> holds if and only if
-      <span class="MathJax_Preview">\rho(a) \in Activities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-444-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-444">\rho(a) \in Activities</script>.</li>
-      <li><span class="MathJax_Preview">W,\rho\models typeOf(ag,agent)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-445-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-445">W,\rho\models typeOf(ag,agent)</script> holds if and only if
-      <span class="MathJax_Preview">\rho(ag) \in Agents</span><span class="MathJax MathJax_Processing" id="MathJax-Element-446-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-446">\rho(ag) \in Agents</script>.</li>
-      <li><span class="MathJax_Preview">W,\rho\models typeOf(c,prov:Collection)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-447-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-447">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
+    <ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-441-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7894"><span style="display: inline-block; position: relative; width: 183px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7895"><span class="mi" id="MathJax-Span-7896" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7897" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7898" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7899" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7900" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7901" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-7902" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7903" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7904" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7905" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7906" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7907" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7908" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7909" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-7910" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7911" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7912" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7913" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7914" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7915" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-441">W,\rho\models typeOf(e,entity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-442-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7916"><span style="display: inline-block; position: relative; width: 111px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7917"><span class="mi" id="MathJax-Span-7918" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7919" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7920" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7921" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7922" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7923" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7924" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7925" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7926" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7927" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7928" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7929" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7930" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-442">\rho(e) \in Entities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-443-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7931"><span style="display: inline-block; position: relative; width: 198px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7932"><span class="mi" id="MathJax-Span-7933" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7934" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7935" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7936" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7937" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7938" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-7939" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7940" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7941" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7942" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7943" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7944" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-7945" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7946" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7947" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7948" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7949" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7950" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7951" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7953" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-7954" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-443">W,\rho\models typeOf(a,activity)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-444-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7955"><span style="display: inline-block; position: relative; width: 124px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7956"><span class="mi" id="MathJax-Span-7957" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7958" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7959" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-7960" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7961" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7962" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-7963" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7964" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7965" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7966" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7967" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7968" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7969" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7970" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7971" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-444">\rho(a) \in Activities</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-445-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7972"><span style="display: inline-block; position: relative; width: 196px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7973"><span class="mi" id="MathJax-Span-7974" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7975" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7976" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7977" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7978" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7979" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-7980" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7981" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7982" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7983" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7984" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7985" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7986" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-7987" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7988" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7989" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7990" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7991" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7992" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-7993" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-445">W,\rho\models typeOf(ag,agent)</script> holds if and only if
+      <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-446-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7994"><span style="display: inline-block; position: relative; width: 118px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7995"><span class="mi" id="MathJax-Span-7996" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-7997" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7998" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7999" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-8000" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8001" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-8002" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-8003" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8004" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8005" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8006" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8007" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-446">\rho(ag) \in Agents</script>.</li>
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-447-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8008"><span style="display: inline-block; position: relative; width: 274px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-8009"><span class="mi" id="MathJax-Span-8010" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-8011" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8012" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-8013" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-8014" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8015" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-8016" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-8017" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8018" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-8019" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-8020" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8021" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-8022" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8023" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-8024" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8025" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8026" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-8027" style="font-family: STIXGeneral-Regular; padding-left: 6px;">:</span><span class="mi" id="MathJax-Span-8028" style="font-family: STIXGeneral-Italic; padding-left: 6px;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8029" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8030" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8031" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8032" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8033" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-8034" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8035" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8036" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8037" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8038" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-447">W,\rho\models typeOf(c,prov:Collection)</script> holds if and only if
       TODO.</li>
-      <li><span class="MathJax_Preview">W,\rho\models typeOf(c,prov:EmptyCollection)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-448-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-448">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
+      <li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-448-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8039"><span style="display: inline-block; position: relative; width: 324px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-8040"><span class="mi" id="MathJax-Span-8041" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-8042" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8043" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-8044" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-8045" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8046" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-8047" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-8048" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8049" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-8050" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-8051" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8052" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-8053" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8054" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-8055" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8056" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8057" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-8058" style="font-family: STIXGeneral-Regular; padding-left: 6px;">:</span><span class="mi" id="MathJax-Span-8059" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8060" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-8061" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-8062" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8063" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-8064" style="font-family: STIXGeneral-Italic;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8065" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8066" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8067" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8068" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8069" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-8070" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8071" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8072" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8073" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8074" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-448">W,\rho\models typeOf(c,prov:EmptyCollection)</script> holds if and only if
       TODO.</li>
       </ol>
       
@@ -2129,14 +2119,7 @@
 <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 class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-449-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-449">\begin{array}[t]{l}
+<div class="inference" number="5" id="communication-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#communication-generation-use-inference">Inference 5 (communication-generation-use-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-449-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8075"><span style="display: inline-block; position: relative; width: 631px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8076"><span class="mtable" id="MathJax-Span-8077" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 625px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 625px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8078"><span class="mrow" id="MathJax-Span-8079"><span class="mi" id="MathJax-Span-8080" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8081" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8082" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8083" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8084" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8085" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8086" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8087" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8088" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8089" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8090" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8091" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8092" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8093" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8094" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8095" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8096" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8097" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8098" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-8099"><span class="mrow" id="MathJax-Span-8100"><span class="mspace" id="MathJax-Span-8101" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8102" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8103" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8104" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8105" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-8106" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8107" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-8108" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8109" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8110" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-8111" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8112" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8113" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8114" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8116" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8117" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8118" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8119" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8120" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8121" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8122" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8123" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8124" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8125" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8126" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8127" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8128" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8129" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8130" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8131" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8132" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-8133"><span class="mrow" id="MathJax-Span-8134"><span class="mspace" id="MathJax-Span-8135" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8136" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8137" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8138" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-8139" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8140" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-8141" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8142" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8143" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8144" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8145" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8146" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8147" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8148" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-8149" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8150" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-8151" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8152" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8153" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8154" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8155" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8156" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8157" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8158" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8159" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8160" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-8161" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8162" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8163" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8164" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8165" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8166" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8167" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8168" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8169" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8170" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8171" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8172" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8173" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8174" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8175" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8176" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8177" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8178" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8179" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8180" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8181" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8182" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8183" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8184" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8185" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8186" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8187" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8188" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8189" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8190" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-8191" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8192" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8193" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8194" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8195" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8196" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8197" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-8198" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8199" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8200" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8201" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8202" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8203" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8204" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8205" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8206" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8207" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8208" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8209" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8210" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8211" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-449">\begin{array}[t]{l}
 \forall id,a_2,a_1,attrs.~
 \\
 \qquad wasInformedBy(id,a_2,a_1,attrs)
@@ -2144,14 +2127,7 @@
 \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 class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-450-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-450">\begin{array}[t]{l}
+<div class="inference" number="6" id="generation-use-communication-inference"><div class="ruleTitle"><a class="internalDFN" href="#generation-use-communication-inference">Inference 6 (generation-use-communication-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-450-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8212"><span style="display: inline-block; position: relative; width: 544px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8213"><span class="mtable" id="MathJax-Span-8214" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 538px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.9px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 538px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8215"><span class="mrow" id="MathJax-Span-8216"><span class="mi" id="MathJax-Span-8217" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8218" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8219" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8220" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8221" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8222" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8223" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8224" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8225" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8226" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8227" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8228" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8229" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8230" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8231" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8232" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8233" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8235" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-8236"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8237" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-8238" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8239" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8240" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="msubsup" id="MathJax-Span-8241"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8242" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-8243" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8244" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8245" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8246" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8247" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8248" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8249" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8250" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8251" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8252" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8253" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8254" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8255" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8256" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-8257"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8258" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-8259" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8260" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8261" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-8262"><span class="mrow" id="MathJax-Span-8263"><span class="mspace" id="MathJax-Span-8264" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8265" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8266" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8267" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8268" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-8269" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8270" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8271" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8272" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8273" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8274" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8275" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8276" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8277" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8278" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8279" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8280" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8281" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8282" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8283" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8284" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8285" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8286" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8287" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8288" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8289" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8290" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8291" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8292" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8293" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8294" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8296" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8297" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-8298"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8299" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-8300" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8301" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8302" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8303" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-8304" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8305" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8306" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8307" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8308" style="font-family: STIXGeneral-Italic;">i</span><span class="msubsup" id="MathJax-Span-8309"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8310" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-8311" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8312" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8313" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8314" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8315" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8316" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8317" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8318" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8319" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8320" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8321" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8322" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8323" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8324" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8325" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8326" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-8327"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8328" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-8329" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8330" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-8331"><span class="mrow" id="MathJax-Span-8332"><span class="mspace" id="MathJax-Span-8333" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8334" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8335" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8336" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8337" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8338" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8339" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8340" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8341" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8342" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8343" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-8344" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8345" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-8346" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8347" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8348" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-8349" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8350" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8351" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8352" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8353" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8354" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8355" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8356" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8357" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8358" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8359" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8360" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8361" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8362" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8363" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8364" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8365" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8366" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8367" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-450">\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)
@@ -2159,14 +2135,7 @@
 \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 class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-451-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-451">\begin{array}[t]{l}
+<div class="inference" number="7" id="entity-generation-invalidation-inference"><div class="ruleTitle"><a class="internalDFN" href="#entity-generation-invalidation-inference">Inference 7 (entity-generation-invalidation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-451-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8368"><span style="display: inline-block; position: relative; width: 768px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8369"><span class="mtable" id="MathJax-Span-8370" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 762px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 762px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8371"><span class="mrow" id="MathJax-Span-8372"><span class="mi" id="MathJax-Span-8373" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8374" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-8375" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8376" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8377" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8378" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8379" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8380" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8381" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8382" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 55px -9px); top: -23.5px; left: 0px;"><span class="mtd" id="MathJax-Span-8383"><span class="mrow" id="MathJax-Span-8384"><span class="mspace" id="MathJax-Span-8385" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8386" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8387" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8388" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8389" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8390" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8391" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8392" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8393" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-8394" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8395" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8396" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8397" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8398" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8399" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8400" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.5px; left: 0px;"><span class="mtd" id="MathJax-Span-8401"><span class="mrow" id="MathJax-Span-8402"><span class="mspace" id="MathJax-Span-8403" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8404" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8405" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8406" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8407" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8408" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8409" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8410" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8411" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8412" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8413" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8414" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8415" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8416" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8417" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8418" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-8419" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8420" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-8421" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8422" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8423" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8424" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8425" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8426" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8427" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8428" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8429" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8430" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8431" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8432" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8433" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8434" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-8435" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8436" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8437" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8438" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8439" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8441" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8442" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8443" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8444" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8445" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8446" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8447" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8448" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8449" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8450" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8451" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8452" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8453" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8454" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8455" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8456" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8457" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8458" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8459" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8460" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8461" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8462" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8463" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8464" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-8465" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8466" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8467" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-8468" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8469" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-8470" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8471" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8472" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8473" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8474" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8475" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8476" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8477" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8478" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8479" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8480" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8481" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8482" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8483" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-8484" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8485" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-8486" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8487" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8488" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8489" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8490" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8491" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8492" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8493" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8494" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8495" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8496" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8497" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-451">\begin{array}[t]{l}
 \forall e,attrs.~
 \\
 \qquad entity(e,attrs)
@@ -2174,14 +2143,7 @@
 \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 class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-452-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-452">\begin{array}[t]{l}
+<div class="inference" number="8" id="activity-start-end-inference"><div class="ruleTitle"><a class="internalDFN" href="#activity-start-end-inference">Inference 8 (activity-start-end-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-452-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8498"><span style="display: inline-block; position: relative; width: 789px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8499"><span class="mtable" id="MathJax-Span-8500" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 783px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.6px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 783px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8501"><span class="mrow" id="MathJax-Span-8502"><span class="mi" id="MathJax-Span-8503" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8504" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-8505" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8506" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8507" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8508" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8509" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8510" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8511" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8512" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8513" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8514" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8515" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8516" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8517" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8518" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8519" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8520" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 55px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-8521"><span class="mrow" id="MathJax-Span-8522"><span class="mspace" id="MathJax-Span-8523" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8524" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8525" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-8526" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8527" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8528" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-8529" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8530" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8531" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8532" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8533" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-8534" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8535" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8536" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8537" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8538" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8539" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8540" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8541" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8542" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8543" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8544" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8545" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8546" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8547" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8548" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.6px; left: 0px;"><span class="mtd" id="MathJax-Span-8549"><span class="mrow" id="MathJax-Span-8550"><span class="mspace" id="MathJax-Span-8551" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8552" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8553" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8554" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8555" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8556" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8557" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8558" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8559" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8560" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8561" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8562" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8563" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8564" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8565" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8566" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8567" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8568" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-8569" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8570" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8571" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8572" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8573" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8574" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8575" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8576" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8577" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8578" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8579" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8580" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8581" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8582" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8583" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8584" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-8585" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8586" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8587" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8588" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8589" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8590" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8591" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8592" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8593" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8594" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8595" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8596" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8597" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8598" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8599" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8600" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8601" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8602" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8603" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8604" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8605" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8606" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8607" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8608" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8609" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8610" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8611" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8612" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8613" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8614" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8615" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8616" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8617" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8618" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-8619" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8620" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8621" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8622" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8623" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8624" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8625" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8626" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8627" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8628" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8629" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8630" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8631" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8632" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8633" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8634" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8635" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8636" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8637" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8638" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8639" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8640" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8641" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8642" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8643" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8644" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8645" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8646" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8647" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8648" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8649" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-452">\begin{array}[t]{l}
 \forall a,t_1,t_2,attrs.~
 \\
 \qquad activity(a,t_1,t_2,attrs)
@@ -2189,14 +2151,7 @@
 \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 class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-453-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-453">\begin{array}[t]{l}
+<div class="inference" number="9" id="wasStartedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-inference">Inference 9 (wasStartedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-453-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8650"><span style="display: inline-block; position: relative; width: 391px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8651"><span class="mtable" id="MathJax-Span-8652" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 385px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 385px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8653"><span class="mrow" id="MathJax-Span-8654"><span class="mi" id="MathJax-Span-8655" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8656" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8657" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8658" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8659" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8660" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8661" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8662" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8663" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8664" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8665" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8666" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8667" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8668" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8669" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8670" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8671" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8672" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8673" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8674" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8675" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8676" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8677" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-8678"><span class="mrow" id="MathJax-Span-8679"><span class="mspace" id="MathJax-Span-8680" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8681" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8682" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8683" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8684" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-8685" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8686" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8687" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8688" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8689" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8690" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8691" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8692" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8693" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8694" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8695" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8696" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8697" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8698" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8699" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8700" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8701" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8702" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8703" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8704" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8705" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8706" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8707" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8708" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8709" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8710" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8711" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8712" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8713" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8714" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-8715"><span class="mrow" id="MathJax-Span-8716"><span class="mspace" id="MathJax-Span-8717" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8718" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8719" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8720" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8721" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8722" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8723" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8724" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8725" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8726" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8727" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8728" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8729" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8730" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8731" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8732" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-8733" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8734" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8735" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8736" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8737" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8738" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8739" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8740" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8741" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8742" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8743" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8744" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8745" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8746" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8747" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8748" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8749" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8750" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8751" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8752" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8753" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8754" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8755" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8756" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8757" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8758" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8759" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8760" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8761" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8762" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-453">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(id,a,e_1,a_1,t,attrs)
@@ -2204,14 +2159,7 @@
 \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 class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-454-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-454">\begin{array}[t]{l}
+<div class="inference" number="10" id="wasEndedBy-inference"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-inference">Inference 10 (wasEndedBy-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-454-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8763"><span style="display: inline-block; position: relative; width: 391px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8764"><span class="mtable" id="MathJax-Span-8765" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 385px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 385px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8766"><span class="mrow" id="MathJax-Span-8767"><span class="mi" id="MathJax-Span-8768" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8769" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8770" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8771" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8772" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8773" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8774" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8775" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8776" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8777" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8778" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8779" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8780" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8781" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8782" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8783" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8784" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8785" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8786" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8787" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8788" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8789" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8790" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-8791"><span class="mrow" id="MathJax-Span-8792"><span class="mspace" id="MathJax-Span-8793" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8794" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8795" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8796" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8797" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8798" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8799" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8800" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8801" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8802" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8803" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8804" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8805" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8806" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8807" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8808" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8809" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8810" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8811" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8812" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8813" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8814" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8815" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8816" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8817" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8818" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-8819" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8820" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8821" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8822" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8823" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8824" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8825" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-8826"><span class="mrow" id="MathJax-Span-8827"><span class="mspace" id="MathJax-Span-8828" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-8829" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-8830" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-8831" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8832" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8833" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8834" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8835" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8837" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8838" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8839" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-8840" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-8841" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8842" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8843" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-8844" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8845" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8846" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8847" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8848" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8849" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8850" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8851" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8852" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-8853" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-8854" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8855" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8856" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8857" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-8858" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8859" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8860" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8861" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8862" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8863" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8864" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8865" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8866" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8867" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-8869" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8870" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-8871" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-8872" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-8873" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-454">\begin{array}[t]{l}
 \forall id,a,e_1,a_1,t,attrs.~
 \\
 \qquad wasEndedBy(id,a,e_1,a_1,t,attrs)
@@ -2219,14 +2167,7 @@
 \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 class="internalDFN" href="#derivation-generation-use-inference">Inference 11 (derivation-generation-use-inference)</a></div><p>In this inference, none of <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-455-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-455">a</script>,<span class="MathJax_Preview">gen_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-456-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-456">gen_2</script>, or <span class="MathJax_Preview">use_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-457-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-457">use_1</script> can be placeholders -.</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-458-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-458">\begin{array}[t]{l}
+<div class="inference" number="11" id="derivation-generation-use-inference"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-use-inference">Inference 11 (derivation-generation-use-inference)</a></div><p>In this inference, none of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-455-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8874"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-8875"><span class="mi" id="MathJax-Span-8876" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-455">a</script>,<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-456-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8877"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-8878"><span class="mi" id="MathJax-Span-8879" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8880" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-8881"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8882" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8883" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-456">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-457-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8884"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 53.9px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-8885"><span class="mi" id="MathJax-Span-8886" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8887" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-8888"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8889" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8890" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-457">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-458-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-8891"><span style="display: inline-block; position: relative; width: 760px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-8892"><span class="mtable" id="MathJax-Span-8893" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 754px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 754px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-8894"><span class="mrow" id="MathJax-Span-8895"><span class="mi" id="MathJax-Span-8896" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-8897" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8898" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8899" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8900" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8901" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8902" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8903" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8904" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8905" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8906" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8907" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8908" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-8909" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8910" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-8911" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-8912"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8913" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8914" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8915" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8916" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-8917" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-8918"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8919" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8920" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8921" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8922" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-8923" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8924" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8925" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8926" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-8927" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-8928" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-8929"><span class="mrow" id="MathJax-Span-8930"><span class="mspace" id="MathJax-Span-8931" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-8932" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-8933" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8934" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8935" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-8936" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8937" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8938" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-8939" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8940" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-8941" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8942" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8943" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-8944" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8945" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8946" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-8947" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8948" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8949" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-8950" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8951" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-8952" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-8953"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8954" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-8955" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8956" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8957" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8958" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-8959" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8960" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-8961" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-8962" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8963" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-8964" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-8965" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8966" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-8967" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-8968"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8969" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8970" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8971" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-8972" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-8973" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-8974" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-8975" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-8976" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-8977" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8978" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8980" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-8981" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-8982" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-8983" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-8984" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-8985" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-8986" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-8987" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-8988" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-8989" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-8990" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8991" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8992" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8993" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8994" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-8995" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-8996" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-8997" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-8998" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-8999" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9000" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9001" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-9002" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-9003"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9004" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9005" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9006" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9007" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-9008" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-9009"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9010" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9011" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9012" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9013" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9014" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9015" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9016" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9017" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9018" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-9019"><span class="mrow" id="MathJax-Span-9020"><span class="mspace" id="MathJax-Span-9021" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9022" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9023" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="msubsup" id="MathJax-Span-9024"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9025" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-9026" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9027" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9028" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9029" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-9030" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9031" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9032" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-9033" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9034" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9035" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9036" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9037" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9038" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9039" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-9040"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9041" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9042" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9043" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9044" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9045" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9046" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9047" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9048" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9049" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9050" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9051" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-9052" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9053" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9054" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9055" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9056" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-9057" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-9058" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-9059" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9060" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9061" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-9062" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9063" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9064" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9065" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9066" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9068" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9069" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9070" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9071" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9072" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9073" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-9074" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-9075"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9076" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9077" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9078" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9079" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9080" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9081" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9082" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9083" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9084" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9085" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9086" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-9087" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9088" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9089" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9090" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9091" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-458">\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)
@@ -2234,14 +2175,7 @@
 \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 class="internalDFN" href="#revision-is-alternate-inference">Inference 12 (revision-is-alternate-inference)</a></div><p>In this inference, any of <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-459-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-459">a</script>,<span class="MathJax_Preview">gen_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-460-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-460">gen_2</script>, or <span class="MathJax_Preview">use_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-461-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-461">use_1</script> can be placeholders -.</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-462-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-462">\begin{array}[t]{l}
+<div class="inference" number="12" id="revision-is-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#revision-is-alternate-inference">Inference 12 (revision-is-alternate-inference)</a></div><p>In this inference, any of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-459-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9092"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-9093"><span class="mi" id="MathJax-Span-9094" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-459">a</script>,<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-460-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9095"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-9096"><span class="mi" id="MathJax-Span-9097" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-9098" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-9099"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9100" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9101" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-460">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-461-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9102"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 53.9px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-9103"><span class="mi" id="MathJax-Span-9104" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9105" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-9106"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9107" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9108" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-461">use_1</script> can be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-462-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9109"><span style="display: inline-block; position: relative; width: 572px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9110"><span class="mtable" id="MathJax-Span-9111" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 566px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.9px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 566px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9112"><span class="mrow" id="MathJax-Span-9113"><span class="mi" id="MathJax-Span-9114" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9115" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9116" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9117" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9118" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9119" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9120" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9121" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9122" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9123" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9124" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9125" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9126" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9127" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9128" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-9129" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9130" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-9131" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9132" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-9133"><span class="mrow" id="MathJax-Span-9134"><span class="mspace" id="MathJax-Span-9135" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9136" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9137" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9138" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9139" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-9140" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9141" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9142" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9143" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-9144" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9145" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9146" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-9147" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9148" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9149" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-9150" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9151" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9152" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9153" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9154" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9155" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9156" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9157" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9158" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9159" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9160" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9161" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9162" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9163" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9164" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-9165" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9166" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-9167" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9168" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mi" id="MathJax-Span-9169" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-9170" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9171" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9172" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-9173" style="font-family: STIXGeneral-Regular; padding-left: 6px;">:</span><span class="mi" id="MathJax-Span-9174" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9175" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-9176" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-9177" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-9178" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-9179" style="font-family: STIXGeneral-Italic; padding-left: 6px;">p</span><span class="mi" id="MathJax-Span-9180" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9181" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9182" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-9183" style="font-family: STIXGeneral-Regular; padding-left: 6px;">:</span><span class="mi" id="MathJax-Span-9184" style="font-family: STIXGeneral-Italic; padding-left: 6px;">R</span><span class="mi" id="MathJax-Span-9185" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9186" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-9187" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9188" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9189" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9190" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9191" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-9192" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9193" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-9194" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-9195"><span class="mrow" id="MathJax-Span-9196"><span class="mspace" id="MathJax-Span-9197" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9198" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9199" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-9200" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9201" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9202" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9203" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9204" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9205" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9206" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9207" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9208" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-9209" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-9210" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-9211"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9212" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9213" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9214" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9215" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9216" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-9217" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9218" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-462">\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]))
@@ -2249,14 +2183,7 @@
 \quad\Rightarrow
 alternateOf(e_2,e_1)
 \end{array}</script></div>
-<div class="inference" number="13" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-463-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-463">\begin{array}[t]{l}
+<div class="inference" number="13" id="attribution-inference"><div class="ruleTitle"><a class="internalDFN" href="#attribution-inference">Inference 13 (attribution-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-463-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9219"><span style="display: inline-block; position: relative; width: 762px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9220"><span class="mtable" id="MathJax-Span-9221" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 756px; height: 0px;"><span style="position: absolute; clip: rect(72.2px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 756px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9222"><span class="mrow" id="MathJax-Span-9223"><span class="mi" id="MathJax-Span-9224" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9226" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9227" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9228" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9229" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9230" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9231" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9232" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-9233" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9234" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9235" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9236" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9237" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9238" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9239" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9240" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-9241"><span class="mrow" id="MathJax-Span-9242"><span class="mspace" id="MathJax-Span-9243" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9244" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9245" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9246" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9247" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-9248" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9250" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9251" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9252" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-9253" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9254" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9255" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9256" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9257" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-9258" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-9259" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9260" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9261" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9262" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9263" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9264" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9265" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9266" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9267" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-9268" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9269" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9270" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9271" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9272" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9273" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9274" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-9275"><span class="mrow" id="MathJax-Span-9276"><span class="mspace" id="MathJax-Span-9277" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9278" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9279" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-9280" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-9281" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9282" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9283" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9284" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-9285" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9286" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-9287" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9288" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9290" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9291" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9292" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-9293" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9294" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-9295" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-9296" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9297" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-9298" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9299" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9300" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9301" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-9302" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9303" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9304" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9305" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9306" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9307" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9308" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9309" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9310" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9311" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9312" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9313" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-9314" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9315" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-9316" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9317" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9318" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9319" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9320" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9321" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9322" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9323" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9324" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9325" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-9326" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-9327" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-9328" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9329" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9330" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-9331" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9332" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9333" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9334" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9335" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9336" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9337" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9338" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9339" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9340" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-9341" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9342" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9343" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-9344" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9345" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9346" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9347" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9348" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9349" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-9350" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9351" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9352" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9353" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9354" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-9355" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9356" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-9357" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-9358" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9359" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9360" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9361" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-463">\begin{array}[t]{l}
 \forall att,e,ag,attrs.~
 \\
 \qquad wasAttributedTo(att,e,ag,attrs)
@@ -2264,14 +2191,7 @@
 \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 class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-464-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-464">\begin{array}[t]{l}
+<div class="inference" number="14" id="delegation-inference"><div class="ruleTitle"><a class="internalDFN" href="#delegation-inference">Inference 14 (delegation-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-464-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9362"><span style="display: inline-block; position: relative; width: 800px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 101.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9363"><span class="mtable" id="MathJax-Span-9364" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 794px; height: 0px;"><span style="position: absolute; clip: rect(73.8px 19360px 150.9px -9px); top: -90px; left: 0px;"><span style="display: inline-block; position: relative; width: 794px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9365"><span class="mrow" id="MathJax-Span-9366"><span class="mi" id="MathJax-Span-9367" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9368" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9369" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9370" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9371" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9372"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9373" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9374" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9375" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9376" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9377"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9378" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9379" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9380" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9381" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9382" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9383" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9384" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9385" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9386" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9387" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9388" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9389" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -21.4px; left: 0px;"><span class="mtd" id="MathJax-Span-9390"><span class="mrow" id="MathJax-Span-9391"><span class="mspace" id="MathJax-Span-9392" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9393" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9394" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9395" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9396" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9397" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9398" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-9399" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9400" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9401" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9402" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-9403" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9404" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9405" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-9406" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-9407" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-9408" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9409" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9410" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9411" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9412" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9413"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9414" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9415" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9416" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9417" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9418"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9419" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9420" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9421" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9422" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9423" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9424" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9425" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9426" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9427" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9428" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9429" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56.7px -9px); top: 4.2px; left: 0px;"><span class="mtd" id="MathJax-Span-9430"><span class="mrow" id="MathJax-Span-9431"><span class="mspace" id="MathJax-Span-9432" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9433" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9434" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∃</span><span class="mi" id="MathJax-Span-9435" style="font-family: STIXGeneral-Italic;">i</span><span class="msubsup" id="MathJax-Span-9436"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9437" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-9438" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9439" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9440" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="msubsup" id="MathJax-Span-9441"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9442" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5px;"><span class="mn" id="MathJax-Span-9443" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9444" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9445" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="msubsup" id="MathJax-Span-9446"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9447" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-9448" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9449" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9450" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="msubsup" id="MathJax-Span-9451"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9452" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5px;"><span class="mn" id="MathJax-Span-9453" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9454" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9455" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span><span class="mi" id="MathJax-Span-9456" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9457" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9458" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9459" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-9460" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9461" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9462" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9463" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9464" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9465" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9466" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9467" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9468" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9469" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-9470" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9471" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9472" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-9473" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9474" style="font-family: STIXGeneral-Italic;">i</span><span class="msubsup" id="MathJax-Span-9475"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9476" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-9477" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9478" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9479" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9480" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9481" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9482"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9483" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9484" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9485" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9486" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="msubsup" id="MathJax-Span-9487"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9488" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5px;"><span class="mn" id="MathJax-Span-9489" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9490" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9491" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9492" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9493" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-9494" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-9495" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-9496" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9497" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9498" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-9499" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9500" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9501" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-9502" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9504" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9505" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9506" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9507" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9508" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-9509" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9510" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9511" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-9512" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9513" style="font-family: STIXGeneral-Italic;">i</span><span class="msubsup" id="MathJax-Span-9514"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9515" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-9516" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9517" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9518" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9519" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9520" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-9521"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9522" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-9523" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9524" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9525" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="msubsup" id="MathJax-Span-9526"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9527" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5px;"><span class="mn" id="MathJax-Span-9528" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9529" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-9530" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">[</span><span class="mo" id="MathJax-Span-9531" style="font-family: STIXGeneral-Regular;">]</span><span class="mo" id="MathJax-Span-9532" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 90px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 75.4px; vertical-align: -58.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-464">\begin{array}[t]{l}
 \forall id,ag_1,ag_2,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_1,ag_2,a,attrs)
@@ -2279,140 +2199,70 @@
 \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 class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="inference" number="15" id="influence-inference"><div class="ruleTitle"><a class="internalDFN" href="#influence-inference">Inference 15 (influence-inference)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-465-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9533"><span style="display: inline-block; position: relative; width: 299px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9534"><span class="mtable" id="MathJax-Span-9535" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 293px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.6px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 293px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9536"><span class="mrow" id="MathJax-Span-9537"><span class="mi" id="MathJax-Span-9538" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9539" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9540" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9541" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9542" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9543" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9544" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9545" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9546" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9547" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9548" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9549" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9550" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9551" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9552" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9553" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9554" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-9555"><span class="mrow" id="MathJax-Span-9556"><span class="mspace" id="MathJax-Span-9557" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9558" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9559" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9560" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9561" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-9562" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9563" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9564" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9565" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9566" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9567" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9568" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9569" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9570" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9571" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9572" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9573" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9574" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9575" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9576" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9577" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9578" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9579" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9580" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9581" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9582" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9583" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9584" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9585" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9586" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9587" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.6px; left: 0px;"><span class="mtd" id="MathJax-Span-9588"><span class="mrow" id="MathJax-Span-9589"><span class="mspace" id="MathJax-Span-9590" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9591" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9592" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-9593" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9594" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9595" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-9596" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9597" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-9598" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9599" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9600" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9601" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9602" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9603" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9604" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9605" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9606" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9607" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9608" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9609" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9610" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9611" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9612" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9613" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9614" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9615" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9616" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9617" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9618" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9619" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9620" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-465">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-465-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-465">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-466-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-466">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-466-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9621"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9622"><span class="mtable" id="MathJax-Span-9623" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 284px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 284px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9624"><span class="mrow" id="MathJax-Span-9625"><span class="mi" id="MathJax-Span-9626" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9627" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9628" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9629" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9630" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-9631" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9632" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9633" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9634" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9635" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9636" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9637" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9638" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9639" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9640" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9641" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9642" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-9643"><span class="mrow" id="MathJax-Span-9644"><span class="mspace" id="MathJax-Span-9645" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9646" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9647" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9648" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9649" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9650" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9651" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9652" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9653" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9654" style="font-family: STIXGeneral-Italic; 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padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-9671" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9672" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9673" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-9674" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9675" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-9676" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9677" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9678" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9679" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9680" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9681" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9682" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; 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position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9713" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9714" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9715" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9716" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9717" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9718" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9742" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9743" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9744" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9745" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9746" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9747" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9748" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9749" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9750" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9751" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9752" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9753" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-9762" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9763" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9764" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-9765" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9766" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-9767" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9768" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9769" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9770" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9771" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9772" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9773" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; 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width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9782" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9783" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9784" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9785" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9786" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9787" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9788" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9789" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9790" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9791" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9792" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9793" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-467">\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)
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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-468-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-9794"><span style="display: inline-block; position: relative; width: 310px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-9795"><span class="mtable" id="MathJax-Span-9796" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 304px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 304px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-9797"><span class="mrow" id="MathJax-Span-9798"><span class="mi" id="MathJax-Span-9799" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-9800" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9801" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9802" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9803" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9804" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9805" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9806" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9807" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9808" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9809" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9810" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9811" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9812" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9813" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9814" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9815" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9816" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9817" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9818" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9819" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9820" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-9821" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-9822"><span class="mrow" id="MathJax-Span-9823"><span class="mspace" id="MathJax-Span-9824" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-9825" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-9826" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9827" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9828" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-9829" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9830" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9831" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9832" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9833" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9834" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9835" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9836" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9837" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9838" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9839" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9840" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9841" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9842" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9843" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9844" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9845" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9846" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9847" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9848" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9849" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9850" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9851" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-9852" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9853" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9854" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9856" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9857" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9858" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-9859"><span class="mrow" id="MathJax-Span-9860"><span class="mspace" id="MathJax-Span-9861" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-9862" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-9863" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-9864" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-9865" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-9866" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-9867" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9868" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-9869" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-9870" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-9871" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9872" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-9873" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-9874" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-9875" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-9876" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-9877" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-9878" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-9879" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-9880" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9881" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9882" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9883" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9884" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9885" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9886" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9887" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9888" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-9889" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9890" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-9891" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-9892" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-9893" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-468">\begin{array}[t]{l}
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 \\
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overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-9902" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9903" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9904" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9905" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9906" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9907" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-9908" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-9909" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-9910" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-9911" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-9912" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-9913" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10045" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10046" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10047" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10048" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.6px; left: 0px;"><span class="mtd" id="MathJax-Span-10049"><span class="mrow" id="MathJax-Span-10050"><span class="mspace" id="MathJax-Span-10051" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10052" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10053" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-10054" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10055" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10056" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-10057" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10058" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-10059" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10060" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-10061" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10062" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10063" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-10064" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10065" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10066" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-10067" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-10068" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10069" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10070" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10071" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10072" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10073" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10074" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-10075" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10076" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10077" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10078" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10079" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10080" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10081" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-470">\begin{array}[t]{l}
 \forall id,e,a,t,attrs.~
 \\
 \qquad wasInvalidatedBy(id,e,a,t,attrs)
 \\
 \quad\Rightarrow
 wasInfluencedBy(id,e,a,attrs)
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-470-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-470">\begin{array}[t]{l}
-\forall id,e,a,t,attrs.~
-\\
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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-471-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10082"><span style="display: inline-block; position: relative; width: 359px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10083"><span class="mtable" id="MathJax-Span-10084" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 353px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.9px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 353px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10085"><span class="mrow" id="MathJax-Span-10086"><span class="mi" id="MathJax-Span-10087" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-10088" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10089" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10090" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10091" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10092" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10093" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10094" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10095" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10096" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10097" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10098" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10099" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-10100" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10101" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-10102" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10103" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-10104" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10105" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10107" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10108" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10109" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10110" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10111" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-10112"><span class="mrow" id="MathJax-Span-10113"><span class="mspace" id="MathJax-Span-10114" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10115" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-10116" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10117" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10118" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-10119" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10120" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10122" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-10123" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10124" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10125" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-10126" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10127" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-10128" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-10129" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10130" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10131" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10132" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10133" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10134" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10135" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10136" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10137" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10138" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10139" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10140" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10141" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-10142" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10143" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-10144" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10145" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-10146" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10147" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10149" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10150" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10151" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10152" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-10153"><span class="mrow" id="MathJax-Span-10154"><span class="mspace" id="MathJax-Span-10155" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10156" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10157" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-10158" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10159" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10160" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-10161" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10162" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-10163" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10164" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-10165" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10166" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10167" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-10168" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10169" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10170" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-10171" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-10172" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10173" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10174" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10175" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10176" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10177" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10178" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10179" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10180" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10181" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10182" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10183" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10184" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10185" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10186" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10187" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10188" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10189" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-471">\begin{array}[t]{l}
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 \\
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-\quad\Rightarrow
-wasInfluencedBy(id,e,ag,attrs)
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-475-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-475">\begin{array}[t]{l}
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-472-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10190"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10191"><span class="mi" id="MathJax-Span-10192" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-472">a</script>,<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-473-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10193"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10194"><span class="mi" id="MathJax-Span-10195" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-473">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-474-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10196"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10197"><span class="mi" id="MathJax-Span-10198" style="font-family: STIXGeneral-Italic;">u</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-474">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-475-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10199"><span style="display: inline-block; position: relative; width: 300px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10200"><span class="mtable" id="MathJax-Span-10201" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 294px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.9px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 294px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10202"><span class="mrow" id="MathJax-Span-10203"><span class="mi" id="MathJax-Span-10204" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-10205" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10206" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10207" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10208" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10209" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10210" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10211" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-10212" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10213" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10214" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10215" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10216" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10217" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10218" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10219" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-10220"><span class="mrow" id="MathJax-Span-10221"><span class="mspace" id="MathJax-Span-10222" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10223" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-10224" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10225" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10226" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-10227" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10228" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10229" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10230" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10231" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-10232" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-10233" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10234" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10235" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10236" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-10237" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-10238" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10239" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10240" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10241" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10242" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10243" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10244" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10245" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-10246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10248" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10250" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10251" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10252" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-10253"><span class="mrow" id="MathJax-Span-10254"><span class="mspace" id="MathJax-Span-10255" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10256" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10257" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-10258" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10259" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10260" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-10261" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10262" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-10263" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10264" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-10265" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10266" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10267" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-10268" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10269" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10270" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-10271" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-10272" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10273" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10274" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10275" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10276" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10277" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10278" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10279" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-10280" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10281" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10282" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10283" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10284" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10285" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10286" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-475">\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">pl</span><span class="MathJax MathJax_Processing" id="MathJax-Element-476-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-476">pl</script> may be a placeholder -.</p><span class="MathJax_Preview">\begin{array}[t]{l}
+\end{array}</script></li><li><p>In this rule, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-476-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10287"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10288"><span class="mi" id="MathJax-Span-10289" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-10290" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-476">pl</script> may be a placeholder -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-477-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10291"><span style="display: inline-block; position: relative; width: 340px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10292"><span class="mtable" id="MathJax-Span-10293" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 334px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.9px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 334px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10294"><span class="mrow" id="MathJax-Span-10295"><span class="mi" id="MathJax-Span-10296" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-10297" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10298" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10299" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10300" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-10301" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10302" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10303" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-10304" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10305" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-10306" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-10307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10309" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10310" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10311" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10312" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10313" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10314" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-10315"><span class="mrow" id="MathJax-Span-10316"><span class="mspace" id="MathJax-Span-10317" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10318" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-10319" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10320" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10321" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-10322" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10323" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10324" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-10325" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-10326" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10327" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10328" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10329" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10330" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10331" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-10332" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10333" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10334" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-10335" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10336" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10337" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; 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padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-10460" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10461" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-10462" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-10463" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10464" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-10465" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10466" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-10467" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10468" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10469" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-10470" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10471" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-10472" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-10473" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-10474" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10475" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10476" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-10477" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10478" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-10479"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10480" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-10481" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10482" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10483" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-10484"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10485" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-10486" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10487" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10488" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-10489" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10490" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10491" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10492" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-10493" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 90px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 75.4px; vertical-align: -58.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-478">\begin{array}[t]{l}
 \forall id,ag_2,ag_1,a,attrs.~
 \\
 \qquad actedOnBehalfOf(id,ag_2,ag_1,a,attrs)
@@ -2420,14 +2270,7 @@
 \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 class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall e.~
-\\
-\qquad entity(e)
-\\
-\quad\Rightarrow
-alternateOf(e,e)
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-479-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-479">\begin{array}[t]{l}
+<div class="inference" number="16" id="alternate-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-reflexive">Inference 16 (alternate-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-479-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10494"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10495"><span class="mtable" id="MathJax-Span-10496" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 172px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.2px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 172px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 51.2px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10497"><span class="mrow" id="MathJax-Span-10498"><span class="mi" id="MathJax-Span-10499" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-10500" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10501" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10502" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 55px -9px); top: -24.8px; left: 0px;"><span class="mtd" id="MathJax-Span-10503"><span class="mrow" id="MathJax-Span-10504"><span class="mspace" id="MathJax-Span-10505" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10506" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10507" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10508" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10509" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10510" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10511" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-10512" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10513" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10514" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 0.2px; left: 0px;"><span class="mtd" id="MathJax-Span-10515"><span class="mrow" id="MathJax-Span-10516"><span class="mspace" id="MathJax-Span-10517" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10518" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10519" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-10520" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10521" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10522" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10523" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10524" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10525" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10526" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10527" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10528" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10529" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10530" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10531" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10532" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10533" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10534" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.7px; vertical-align: -54.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-479">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad entity(e)
@@ -2436,17 +2279,10 @@
 alternateOf(e,e)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview">ent = rho(e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-480-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-480">ent = rho(e)</script>.  Clearly <span class="MathJax_Preview">e \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-481-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-481">e \in Entities</script> and
-  <span class="MathJax_Preview">thingOf(e) = thingOf(e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-482-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-482">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview">W,\rho \models alternateOf(e,e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-483-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-483">W,\rho \models alternateOf(e,e)</script>.</p>
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-480-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10535"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10536"><span class="mi" id="MathJax-Span-10537" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10538" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10539" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-10540" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10541" style="font-family: STIXGeneral-Italic; padding-left: 6px;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10542" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10543" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-10544" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10545" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10546" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-480">ent = rho(e)</script>.  Clearly <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-481-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10547"><span style="display: inline-block; position: relative; width: 89px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.3px 19360px 51.5px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10548"><span class="mi" id="MathJax-Span-10549" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10550" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-10551" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10552" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10553" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10554" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10555" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10556" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10557" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10558" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-481">e \in Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-482-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10559"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10560"><span class="mi" id="MathJax-Span-10561" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10562" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10563" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10564" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10565" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10566" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10567" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10568" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10569" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10570" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-10571" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10572" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10573" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10574" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10575" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10576" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10577" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10578" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10579" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10580" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10581" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-482">thingOf(e) = thingOf(e)</script>, so <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-483-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10582"><span style="display: inline-block; position: relative; width: 187px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10583"><span class="mi" id="MathJax-Span-10584" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-10585" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10586" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-10587" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-10588" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-10589" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10590" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10591" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10592" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10593" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10594" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10595" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10596" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10597" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10598" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10599" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-10600" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-10601" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10602" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-10603" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-483">W,\rho \models alternateOf(e,e)</script>.</p>
   </div>
-<div class="inference" number="17" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-484-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-484">\begin{array}[t]{l}
+<div class="inference" number="17" id="alternate-transitive"><div class="ruleTitle"><a class="internalDFN" href="#alternate-transitive">Inference 17 (alternate-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-484-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10604"><span style="display: inline-block; position: relative; width: 357px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10605"><span class="mtable" id="MathJax-Span-10606" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 351px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 145px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 351px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 54.1px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10607"><span class="mrow" id="MathJax-Span-10608"><span class="mi" id="MathJax-Span-10609" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-10610"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10611" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10612" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10613" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10614" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10615" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10616" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10617" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10618" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10619" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10620" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10621" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10622" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-10623"><span class="mrow" id="MathJax-Span-10624"><span class="mspace" id="MathJax-Span-10625" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10626" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10627" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10628" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10629" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10630" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10631" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10632" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10633" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10634" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10635" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10636" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10637" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10638"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10639" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10640" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10641" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10642" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10643" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10644" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10645" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-10646" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-10647" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">a</span><span class="mi" id="MathJax-Span-10648" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10649" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10651" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10652" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10653" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10654" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10655" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10656" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10657" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10658" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10659"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10660" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10661" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10662" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10663" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10664" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10665" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10666" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2px; left: 0px;"><span class="mtd" id="MathJax-Span-10667"><span class="mrow" id="MathJax-Span-10668"><span class="mspace" id="MathJax-Span-10669" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10670" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10671" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-10672" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10673" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10674" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10675" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10676" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10677" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10678" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10679" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10680" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10681" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10682" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10683"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10684" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10685" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10686" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10687" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10688" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10689" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10690" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.5px; vertical-align: -56px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-484">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad alternateOf(e_1,e_2) \wedge alternateOf(e_2,e_3)
@@ -2455,21 +2291,13 @@
 alternateOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview">ent_1 = rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-485-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-485">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-486-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-486">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview">ent_3 = \rho(e_3)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-487-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-487">ent_3 = \rho(e_3)</script>.  Then  by
-  assumption <span class="MathJax_Preview">ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-488-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-488">ent_1</script>, <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-489-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-489">ent_2</script>, and <span class="MathJax_Preview">ent_3</span><span class="MathJax MathJax_Processing" id="MathJax-Element-490-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-490">ent_3</script> are in <span class="MathJax_Preview">Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-491-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-491">Entities</script> and
-  <span class="MathJax_Preview">thingOf(e_1) = thingOf(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-492-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-492">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview">thingOf(e_2) = thingOf(e_3)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-493-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-493">thingOf(e_2) = thingOf(e_3)</script>, so
-  <span class="MathJax_Preview">thingOf(e_1) = thingOf(e_3)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-494-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-494">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview">W,\rho
-  \models alternateOf(e_2,e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-495-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-495">W,\rho
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-485-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10691"><span style="display: inline-block; position: relative; width: 113px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10692"><span class="mi" id="MathJax-Span-10693" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10694" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10695"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10696" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10697" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10698" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10699" style="font-family: STIXGeneral-Italic; padding-left: 6px;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10700" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10701" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-10702" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10703"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10704" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10705" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10706" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-485">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-486-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10707"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10708"><span class="mi" id="MathJax-Span-10709" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10710" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10711"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10712" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10713" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10714" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10715" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-10716" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10717"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10718" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10719" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10720" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-486">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-487-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10721"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10722"><span class="mi" id="MathJax-Span-10723" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10724" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10725"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10726" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10727" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10728" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10729" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-10730" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10731"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10732" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10733" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10734" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-487">ent_3 = \rho(e_3)</script>.  Then  by
+  assumption <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-488-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10735"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10736"><span class="mi" id="MathJax-Span-10737" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10738" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10739"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10740" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10741" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-488">ent_1</script>, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-489-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10742"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10743"><span class="mi" id="MathJax-Span-10744" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10745" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10746"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10747" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10748" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-489">ent_2</script>, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-490-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10749"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 54.1px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10750"><span class="mi" id="MathJax-Span-10751" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10752" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10753"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10754" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10755" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.7px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-490">ent_3</script> are in <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-491-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10756"><span style="display: inline-block; position: relative; width: 58px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.3px 19360px 51.3px -9px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10757"><span class="mi" id="MathJax-Span-10758" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10759" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10760" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10761" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10762" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10764" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10765" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-491">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-492-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10766"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10767"><span class="mi" id="MathJax-Span-10768" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10769" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10770" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10771" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10772" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10773" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10774" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10775" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10776"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10777" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10778" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10779" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-10780" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10781" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10782" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10783" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10784" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10785" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10786" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10787" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10788" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10789"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10790" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10791" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10792" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-492">thingOf(e_1) = thingOf(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-493-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10793"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10794"><span class="mi" id="MathJax-Span-10795" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10796" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10797" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10798" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10799" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10800" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10801" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10802" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10803"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10804" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10805" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10806" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-10807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10809" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10810" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10811" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10812" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10813" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10814" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10815" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10816"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10817" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10818" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10819" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-493">thingOf(e_2) = thingOf(e_3)</script>, so
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-494-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10820"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10821"><span class="mi" id="MathJax-Span-10822" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10823" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10824" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10825" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10826" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10827" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10828" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10829" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10830"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10831" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10832" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10833" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-10834" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10835" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10836" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10837" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10838" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10839" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10840" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10841" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10842" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10843"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10844" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10845" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10846" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-494">thingOf(e_1) = thingOf(e_3)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-495-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10847"><span style="display: inline-block; position: relative; width: 204px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10848"><span class="mi" id="MathJax-Span-10849" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-10850" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-10851" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-10852" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-10853" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-10854" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10856" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10857" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10858" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10860" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10861" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10862" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10863" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10864" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10865"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10866" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10867" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10868" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10869" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10870" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10871" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10872" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-495">W,\rho
   \models alternateOf(e_2,e_1)</script>.</p>
   </div>
-<div class="inference" number="18" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall e_1,e_2.~
-\\
-\qquad alternateOf(e_1,e_2)
-\\
-\quad\Rightarrow
-alternateOf(e_2,e_1)
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-496-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-496">\begin{array}[t]{l}
+<div class="inference" number="18" id="alternate-symmetric"><div class="ruleTitle"><a class="internalDFN" href="#alternate-symmetric">Inference 18 (alternate-symmetric)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-496-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10873"><span style="display: inline-block; position: relative; width: 195px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-10874"><span class="mtable" id="MathJax-Span-10875" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 189px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 189px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-10876"><span class="mrow" id="MathJax-Span-10877"><span class="mi" id="MathJax-Span-10878" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-10879"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10880" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10881" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10882" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10883" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10884" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10885" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10886" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-10887" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-10888"><span class="mrow" id="MathJax-Span-10889"><span class="mspace" id="MathJax-Span-10890" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-10891" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10892" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10893" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10895" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10896" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10897" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10898" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10899" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10900" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10901" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10902" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10903"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10904" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10905" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10906" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10907" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10908" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10909" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10910" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-10911"><span class="mrow" id="MathJax-Span-10912"><span class="mspace" id="MathJax-Span-10913" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-10914" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-10915" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-10916" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-10917" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10918" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10919" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10920" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10921" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-10922" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10923" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10924" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10925" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10926" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10927"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10928" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10929" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10930" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-10931" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10932" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10933" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10934" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-496">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad alternateOf(e_1,e_2)
@@ -2478,21 +2306,13 @@
 alternateOf(e_2,e_1)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview">ent_1 = rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-497-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-497">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-498-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-498">ent_2 = \rho(e_2)</script>.  Then  by
-  assumption both <span class="MathJax_Preview">ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-499-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-499">ent_1</script> and <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-500-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-500">ent_2</script> are in <span class="MathJax_Preview">Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-501-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-501">Entities</script> and
-  <span class="MathJax_Preview">thingOf(e_1) = thingOf(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-502-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-502">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview">W,\rho
-  \models alternateOf(e_2,e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-503-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-503">W,\rho
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-497-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10935"><span style="display: inline-block; position: relative; width: 113px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10936"><span class="mi" id="MathJax-Span-10937" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10938" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10939"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10940" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10941" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10942" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10943" style="font-family: STIXGeneral-Italic; padding-left: 6px;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10944" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10945" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-10946" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10947"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10948" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10949" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10950" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-497">ent_1 = rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-498-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10951"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10952"><span class="mi" id="MathJax-Span-10953" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10954" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10955"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10956" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10957" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10958" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-10959" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-10960" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10961"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10962" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-10963" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-10964" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-498">ent_2 = \rho(e_2)</script>.  Then  by
+  assumption both <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-499-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10965"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10966"><span class="mi" id="MathJax-Span-10967" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10968" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10969"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10970" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10971" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-499">ent_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-500-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10972"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10973"><span class="mi" id="MathJax-Span-10974" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10975" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-10976"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-10977" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-10978" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-500">ent_2</script> are in <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-501-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10979"><span style="display: inline-block; position: relative; width: 58px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.3px 19360px 51.3px -9px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10980"><span class="mi" id="MathJax-Span-10981" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-10982" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10983" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10984" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10985" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10986" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10987" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-10988" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-501">Entities</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-502-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-10989"><span style="display: inline-block; position: relative; width: 207px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-10990"><span class="mi" id="MathJax-Span-10991" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-10992" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-10993" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-10994" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-10995" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-10996" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-10997" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-10998" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-10999"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11000" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11001" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11002" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11003" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11004" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11005" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-11006" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11007" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11008" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-11009" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11010" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11011" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11012"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11013" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11014" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11015" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-502">thingOf(e_1) = thingOf(e_2)</script>, as required to conclude <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-503-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11016"><span style="display: inline-block; position: relative; width: 204px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11017"><span class="mi" id="MathJax-Span-11018" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-11019" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11020" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-11021" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-11022" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-11023" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11024" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11025" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11026" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11027" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11028" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11029" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11030" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11031" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11032" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11033" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11034"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11035" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11036" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11037" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11038" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11039" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11040" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11041" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-503">W,\rho
   \models alternateOf(e_2,e_1)</script>.</p>
   </div>
   
-<div class="inference" number="19" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-504-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-504">\begin{array}[t]{l}
+<div class="inference" number="19" id="specialization-transitive"><div class="ruleTitle"><a class="internalDFN" href="#specialization-transitive">Inference 19 (specialization-transitive)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-504-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11042"><span style="display: inline-block; position: relative; width: 429px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-11043"><span class="mtable" id="MathJax-Span-11044" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 423px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 145px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 423px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 54.1px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-11045"><span class="mrow" id="MathJax-Span-11046"><span class="mi" id="MathJax-Span-11047" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-11048"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11049" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11050" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11051" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11052" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11053" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11054" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11055" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11056" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11057" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11058" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11059" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-11060" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-11061"><span class="mrow" id="MathJax-Span-11062"><span class="mspace" id="MathJax-Span-11063" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-11064" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11065" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-11066" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11067" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11068" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11069" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11070" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11071" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11072" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-11073" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11074" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11075" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11076" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11077" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11078" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11079" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11080" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11081"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11082" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11083" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11084" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11085" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11086" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11087" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11088" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11089" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-11090" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">s</span><span class="mi" id="MathJax-Span-11091" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-11092" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11093" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11094" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11095" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11096" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11097" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11098" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-11099" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11100" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11101" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11102" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11103" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11104" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11105" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11106" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11107"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11108" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11109" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11110" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11111" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11112" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11113" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11114" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2px; left: 0px;"><span class="mtd" id="MathJax-Span-11115"><span class="mrow" id="MathJax-Span-11116"><span class="mspace" id="MathJax-Span-11117" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-11118" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-11119" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-11120" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-11121" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11122" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11123" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11124" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11125" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11126" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11127" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-11128" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11129" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11130" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11131" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11132" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11133" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11134" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11135" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11136"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11137" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11138" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11139" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11140" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11141" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11142" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11143" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.5px; vertical-align: -56px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-504">\begin{array}[t]{l}
 \forall e_1,e_2,e_3.~
 \\
 \qquad specializationOf(e_1,e_2) \wedge specializationOf(e_2,e_3)
@@ -2501,28 +2321,18 @@
 specializationOf(e_1,e_3)
 \end{array}</script></div>
 <div class="proof">
-  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview">ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-505-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-505">ent_1</script> and
-  <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-506-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-506">ent_2</script> and for <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-507-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-507">ent_2</script> and <span class="MathJax_Preview">ent_3</span><span class="MathJax MathJax_Processing" id="MathJax-Element-508-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-508">ent_3</script>, where <span class="MathJax_Preview">ent_1 = \rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-509-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-509">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-510-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-510">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview">ent_3 =
-  \rho(e_3)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-511-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-511">ent_3 =
-  \rho(e_3)</script>. Then <span class="MathJax_Preview">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
-  lifetime(e_3)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-512-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-512">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
+  <p> Suppose the conditions for specialization hold of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-505-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11144"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11145"><span class="mi" id="MathJax-Span-11146" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11147" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11148"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11149" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11150" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-505">ent_1</script> and
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-506-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11151"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11152"><span class="mi" id="MathJax-Span-11153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11154" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11155"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11156" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11157" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-506">ent_2</script> and for <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-507-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11158"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11159"><span class="mi" id="MathJax-Span-11160" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11161" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11162"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11163" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11164" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-507">ent_2</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-508-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11165"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 54.1px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11166"><span class="mi" id="MathJax-Span-11167" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11168" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11169"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11171" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.7px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-508">ent_3</script>, where <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-509-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11172"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11173"><span class="mi" id="MathJax-Span-11174" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11175" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11176"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11177" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11178" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11179" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11180" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11181" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11182"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11183" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11184" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11185" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-509">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-510-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11186"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11187"><span class="mi" id="MathJax-Span-11188" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11189" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11190"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11191" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11192" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11193" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11194" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11195" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11196"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11197" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11198" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11199" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-510">ent_2 = \rho(e_2)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-511-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11200"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11201"><span class="mi" id="MathJax-Span-11202" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11203" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11204"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11205" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11206" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11207" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11208" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11209" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11210"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11211" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11212" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11213" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-511">ent_3 =
+  \rho(e_3)</script>. Then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-512-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11214"><span style="display: inline-block; position: relative; width: 310px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11215"><span class="mi" id="MathJax-Span-11216" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11217" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11218" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-11219" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11220" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11221" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11222" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-11223" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11224" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11225"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11226" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11227" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11228" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11229" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊆</span><span class="mi" id="MathJax-Span-11230" style="font-family: STIXGeneral-Italic; padding-left: 6px;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11231" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11232" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-11233" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11235" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11236" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-11237" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11238" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11239"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11240" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11241" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11242" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11243" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊆</span><span class="mi" id="MathJax-Span-11244" style="font-family: STIXGeneral-Italic; padding-left: 6px;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11245" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11246" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-11247" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11248" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11249" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11250" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-11251" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11252" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11253"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11254" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11255" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11256" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-512">lifetime(e_1) \subseteq lifetime(e_2) \subseteq
   lifetime(e_3)</script>.  Moreover, 
-  <span class="MathJax_Preview">value(obj_2,attr) \supseteq value(obj_3,attr)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-513-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-513">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
-  <span class="MathJax_Preview">value(obj_1,attr)\supseteq value(obj_2,attr)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-514-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-514">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview">value(obj_1,attr)
-  \supseteq value(obj_3,attr)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-515-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-515">value(obj_1,attr)
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-513-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11257"><span style="display: inline-block; position: relative; width: 270px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.9px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11258"><span class="mi" id="MathJax-Span-11259" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-11260" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11261" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11262" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11263" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11264" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11265" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11266" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11267"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11268" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11269" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11270" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11271" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11272" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11273" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11274" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11275" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11276" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-11277" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11278" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11279" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11280" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11281" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11282" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11283" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11284" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11285"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11286" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11287" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11288" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11289" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11290" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11291" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11292" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11293" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 20.1px; vertical-align: -5.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-513">value(obj_2,attr) \supseteq value(obj_3,attr)</script>, and similarly
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-514-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11294"><span style="display: inline-block; position: relative; width: 270px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11295"><span class="mi" id="MathJax-Span-11296" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-11297" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11298" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11299" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11300" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11301" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11302" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11303" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11304"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11305" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11306" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11309" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11310" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11311" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11312" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11313" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-11314" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11315" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11316" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11317" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11318" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11319" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11320" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11321" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11322"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11323" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11324" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11325" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11326" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11327" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11328" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11329" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11330" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-514">value(obj_1,attr)\supseteq value(obj_2,attr)</script> so <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-515-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11331"><span style="display: inline-block; position: relative; width: 270px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.9px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11332"><span class="mi" id="MathJax-Span-11333" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-11334" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11335" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11336" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11337" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11338" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11339" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11340" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11341"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11342" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11343" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11344" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11345" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11346" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11347" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11348" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11349" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11350" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-11351" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11352" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11354" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11355" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11356" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11357" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11358" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-11359"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11360" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-11361" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11362" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11363" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11364" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11365" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11366" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-11367" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 20.1px; vertical-align: -5.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-515">value(obj_1,attr)
   \supseteq value(obj_3,attr)</script>.  (TODO:
-  How do we know <span class="MathJax_Preview">e_3 \neq e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-516-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-516">e_3 \neq e_1</script>?  Need strict ordering on entities in semantics.)
+  How do we know <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-516-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11368"><span style="display: inline-block; position: relative; width: 61px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 54.1px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11369"><span class="msubsup" id="MathJax-Span-11370"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11371" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11372" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">3</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11373" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≠</span><span class="msubsup" id="MathJax-Span-11374" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11375" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11376" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.9px; vertical-align: -4.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-516">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 class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall e_1,e_2.~
-\\
-\qquad specializationOf(e_1,e_2)
-\\
-\quad\Rightarrow
-alternateOf(e_1,e_2)
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-517-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-517">\begin{array}[t]{l}
+<div class="inference" number="20" id="specialization-alternate-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-alternate-inference">Inference 20 (specialization-alternate-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-517-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11377"><span style="display: inline-block; position: relative; width: 230px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-11378"><span class="mtable" id="MathJax-Span-11379" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 224px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 224px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-11380"><span class="mrow" id="MathJax-Span-11381"><span class="mi" id="MathJax-Span-11382" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-11383"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11384" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11385" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11386" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11387" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11388" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11389" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11390" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-11391" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-11392"><span class="mrow" id="MathJax-Span-11393"><span class="mspace" id="MathJax-Span-11394" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-11395" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11396" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-11397" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11398" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11399" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11400" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11401" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11402" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11403" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-11404" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11405" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11406" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11407" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11408" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11409" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11410" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11411" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11412"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11413" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11414" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11415" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11416" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11417" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11418" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11419" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-11420"><span class="mrow" id="MathJax-Span-11421"><span class="mspace" id="MathJax-Span-11422" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-11423" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-11424" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-11425" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11426" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11427" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11428" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11429" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11430" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11431" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11432" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11433" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11434" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11435" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11436"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11437" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11438" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11439" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11440" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11441" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11442" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11443" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-517">\begin{array}[t]{l}
 \forall e_1,e_2.~
 \\
 \qquad specializationOf(e_1,e_2)
@@ -2531,19 +2341,12 @@
 alternateOf(e_1,e_2)
 \end{array}</script></div>
 <div class="proof">
-  <p> If <span class="MathJax_Preview">ent_1=\rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-518-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-518">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-519-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-519">ent_2 = \rho(e_2)</script> are
-  specializations, then <span class="MathJax_Preview">thingOf(ent_1) = thingOf(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-520-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-520">thingOf(ent_1) = thingOf(ent_2)</script>.
+  <p> If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-518-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11444"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11445"><span class="mi" id="MathJax-Span-11446" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11447" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11448"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11449" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11450" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11451" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11452" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11453" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11454"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11455" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11456" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11457" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-518">ent_1=\rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-519-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11458"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11459"><span class="mi" id="MathJax-Span-11460" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11461" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11462"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11463" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11464" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11465" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11466" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11467" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11468"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11469" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11470" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11471" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-519">ent_2 = \rho(e_2)</script> are
+  specializations, then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-520-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11472"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11473"><span class="mi" id="MathJax-Span-11474" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11475" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-11476" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11477" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11478" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-11479" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11480" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11481" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11482" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11483" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11484"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11485" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11486" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11487" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11488" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11489" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11490" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-11491" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11492" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11493" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-11494" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11495" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11496" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11497" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11498" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11499"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11500" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11501" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11502" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-520">thingOf(ent_1) = thingOf(ent_2)</script>.
 </p>
 </div>
 
-<div class="inference" number="21" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-521-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-521">\begin{array}[t]{l}
+<div class="inference" number="21" id="specialization-attributes-inference"><div class="ruleTitle"><a class="internalDFN" href="#specialization-attributes-inference">Inference 21 (specialization-attributes-inference)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-521-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11503"><span style="display: inline-block; position: relative; width: 362px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-11504"><span class="mtable" id="MathJax-Span-11505" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 356px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.6px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 356px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-11506"><span class="mrow" id="MathJax-Span-11507"><span class="mi" id="MathJax-Span-11508" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-11509"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11510" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11511" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11512" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11513" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11514" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11515" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11516" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11517" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11518" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11519" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11520" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11521" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11522" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-11523" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-11524"><span class="mrow" id="MathJax-Span-11525"><span class="mspace" id="MathJax-Span-11526" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-11527" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11528" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11529" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11530" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11531" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11532" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11533" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11534"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11535" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11536" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11537" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11538" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11539" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11540" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11541" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11542" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11543" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11544" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-11545" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">s</span><span class="mi" id="MathJax-Span-11546" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-11547" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11548" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11549" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11550" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11551" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11552" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11553" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-11554" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11555" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11556" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11557" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11558" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11559" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-11560" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-11561" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11562"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11563" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11564" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11565" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11566" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11567" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11568" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11569" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.6px; left: 0px;"><span class="mtd" id="MathJax-Span-11570"><span class="mrow" id="MathJax-Span-11571"><span class="mspace" id="MathJax-Span-11572" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-11573" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-11574" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-11575" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11576" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11577" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11578" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11579" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11580" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11581"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11582" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11583" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11584" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11585" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11586" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11587" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11588" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11589" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11590" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-521">\begin{array}[t]{l}
 \forall e_1,attrs,e_2.~
 \\
 \qquad entity(e_1,attrs) \wedge specializationOf(e_2,e_1)
@@ -2553,12 +2356,12 @@
 \end{array}</script></div>
 </section>
 <div class="proof">
-  <p> Suppose <span class="MathJax_Preview">ent_1 = \rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-522-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-522">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-523-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-523">ent_2 = \rho(e_2)</script>.  Suppose
-  <span class="MathJax_Preview">(att,v)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-524-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-524">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview">attrs</span><span class="MathJax MathJax_Processing" id="MathJax-Element-525-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-525">attrs</script>.  Since
-  <span class="MathJax_Preview">entity(e_1,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-526-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-526">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview">v \in value(ent_1,att)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-527-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-527">v \in value(ent_1,att)</script>.
-  Thus <span class="MathJax_Preview">v \in value(ent_2,att)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-528-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-528">v \in value(ent_2,att)</script> since <span class="MathJax_Preview">value(ent_2,att) \supseteq value(ent_1,att)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-529-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-529">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">attrs</span><span class="MathJax MathJax_Processing" id="MathJax-Element-530-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-530">attrs</script>, and since
-  <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-531-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-531">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview">W,\rho \models entity(e,attrs</span><span class="MathJax MathJax_Processing" id="MathJax-Element-532-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-532">W,\rho \models entity(e,attrs</script>).
+  <p> Suppose <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-522-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11591"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11592"><span class="mi" id="MathJax-Span-11593" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11594" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11595"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11596" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11597" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11598" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11599" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11600" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11601"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11602" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11603" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11604" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-522">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-523-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11605"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11606"><span class="mi" id="MathJax-Span-11607" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11608" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11609"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11610" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11611" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11612" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-11613" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-11614" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11615"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11616" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11617" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11618" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-523">ent_2 = \rho(e_2)</script>.  Suppose
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-524-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11619"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11620"><span class="mo" id="MathJax-Span-11621" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11622" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11623" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11624" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11625" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11626" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">v</span><span class="mo" id="MathJax-Span-11627" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-524">(att,v)</script> is an attribute-value pair in <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-525-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11628"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11629"><span class="mi" id="MathJax-Span-11630" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11631" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11632" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11633" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11634" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-525">attrs</script>.  Since
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-526-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11635"><span style="display: inline-block; position: relative; width: 114px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11636"><span class="mi" id="MathJax-Span-11637" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11638" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11639" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11640" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11641" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11642" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11643" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-11644"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11645" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11646" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11647" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11648" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11649" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11650" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11651" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11652" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11653" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-526">entity(e_1,attrs)</script> holds, we know that <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-527-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11654"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11655"><span class="mi" id="MathJax-Span-11656" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-11657" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-11658" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11659" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11660" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11661" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11662" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11663" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11664" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11665" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11666"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11667" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11668" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11669" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11670" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11671" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11672" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11673" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-527">v \in value(ent_1,att)</script>.
+  Thus <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-528-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11674"><span style="display: inline-block; position: relative; width: 145px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11675"><span class="mi" id="MathJax-Span-11676" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-11677" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-11678" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11679" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11680" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11681" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11682" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11683" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11684" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11685" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11686"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11687" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11688" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11689" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11690" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11691" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11692" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11693" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-528">v \in value(ent_2,att)</script> since <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-529-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11694"><span style="display: inline-block; position: relative; width: 253px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11695"><span class="mi" id="MathJax-Span-11696" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-11697" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11698" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11699" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11700" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11701" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11702" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11703" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11704"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11705" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11706" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11707" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11708" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11709" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11710" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11711" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-11712" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-11713" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-11714" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11715" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-11716" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11717" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11718" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11719" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11720" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-11721"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11722" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11723" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11724" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11725" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11726" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11727" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11728" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-529">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 class="MathJax" id="MathJax-Element-530-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11729"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11730"><span class="mi" id="MathJax-Span-11731" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11732" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11733" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11734" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11735" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-530">attrs</script>, and since
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-531-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11736"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-11737"><span class="msubsup" id="MathJax-Span-11738"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11739" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-11740" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-531">e_2</script> obviously denotes an entity, we can conclude <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-532-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11741"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11742"><span class="mi" id="MathJax-Span-11743" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-11744" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11745" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-11746" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-11747" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-11748" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11749" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11750" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11751" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11752" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11753" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11754" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-11755" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11756" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11757" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11758" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11759" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11760" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-532">W,\rho \models entity(e,attrs</script>).
   </p>
 </div>
 
@@ -2569,44 +2372,37 @@
 
 <div class="constraint" number="22" id="key-object"><div class="ruleTitle"><a class="internalDFN" href="#key-object">Constraint 22 (key-object)</a></div>
   <ol><li>The
-  identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-533-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-533">id</script> is a <span class="conditional">KEY</span> for
-  the <span class="MathJax_Preview">entity(id,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-534-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-534">entity(id,attrs)</script> statement.</li>
-  <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-535-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-535">id</script>
+  identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-533-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11761"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11762"><span class="mi" id="MathJax-Span-11763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11764" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-533">id</script> is a <span class="conditional">KEY</span> for
+  the <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-534-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11765"><span style="display: inline-block; position: relative; width: 113px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11766"><span class="mi" id="MathJax-Span-11767" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11768" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11769" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11770" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11771" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11772" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11773" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11774" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11775" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11776" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11777" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11778" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11779" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11780" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11781" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11782" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-534">entity(id,attrs)</script> statement.</li>
+  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-535-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11783"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11784"><span class="mi" id="MathJax-Span-11785" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11786" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-535">id</script>
   is a <span class="conditional">KEY</span> for the
-  <span class="MathJax_Preview">activity(id,t_1,t_2,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-536-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-536">activity(id,t_1,t_2,attrs)</script> statement.</li>
-  <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-537-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-537">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview">agent(id,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-538-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-538">agent(id,attrs)</script> statement.</li></ol></div>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-536-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11787"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11788"><span class="mi" id="MathJax-Span-11789" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11790" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-11791" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11792" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11793" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-11794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11795" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11796" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11797" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11798" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11799" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11800" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11801" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11802" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11803" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11804" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11805" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11806" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-11807" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11808" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11809" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11810" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11811" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11812" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11813" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11814" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-536">activity(id,t_1,t_2,attrs)</script> statement.</li>
+  <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-537-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11815"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11816"><span class="mi" id="MathJax-Span-11817" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11818" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-537">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-538-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11819"><span style="display: inline-block; position: relative; width: 114px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11820"><span class="mi" id="MathJax-Span-11821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11822" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-11823" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11825" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11826" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11827" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11828" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11829" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11830" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11832" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11833" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11834" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11835" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-538">agent(id,attrs)</script> statement.</li></ol></div>
 <div class="constraint" number="23" id="key-properties"><div class="ruleTitle"><a class="internalDFN" href="#key-properties">Constraint 23 (key-properties)</a></div>
-  <ol><li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-539-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-539">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasGeneratedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-540-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-540">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-541-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-541">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview">used(id,a,e,t,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-542-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-542">used(id,a,e,t,attrs)</script>
+  <ol><li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-539-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11836"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11837"><span class="mi" id="MathJax-Span-11838" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11839" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-539">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-540-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11840"><span style="display: inline-block; position: relative; width: 249px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11841"><span class="mi" id="MathJax-Span-11842" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-11843" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11844" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11845" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-11846" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11847" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11848" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11849" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11850" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11851" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11852" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11853" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-11854" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-11855" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11856" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11857" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11858" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11859" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11860" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-11861" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11862" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-11863" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11864" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11865" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11866" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11867" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11869" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11870" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11871" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-540">wasGeneratedBy(id,e,a,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-541-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11872"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11873"><span class="mi" id="MathJax-Span-11874" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11875" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-541">id</script> is a <span class="conditional">KEY</span> for the <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-542-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11876"><span style="display: inline-block; position: relative; width: 154px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11877"><span class="mi" id="MathJax-Span-11878" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-11879" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11880" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11881" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11882" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11883" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11884" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11885" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11886" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-11887" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11888" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-11889" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11890" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11891" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11892" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11893" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11894" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11895" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11896" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11897" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-542">used(id,a,e,t,attrs)</script>
     statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-543-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-543">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasInformedBy(id,a_2,a_1,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-544-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-544">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-545-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-545">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasStartedBy(id,a_2,e,a_1,t,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-546-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-546">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-547-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-547">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasEndedBy(id,a_2,e,a_1,t,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-548-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-548">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-549-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-549">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasInvalidatedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-550-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-550">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-551-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-551">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-552-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-552">wasDerivedFrom(id,e_2,e_1,a,g_2,u_1,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-553-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-553">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasAttributedTo(id,e,ag,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-554-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-554">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-555-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-555">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasAssociatedWith(id,a,ag,pl,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-556-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-556">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-557-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-557">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-558-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-558">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
-    <li>The identifier field <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-559-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-559">id</script> is a <span class="conditional">KEY</span> for the
-    <span class="MathJax_Preview">wasInfluencedBy(id,o2,o1,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-560-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-560">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-543-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11898"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11899"><span class="mi" id="MathJax-Span-11900" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11901" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-543">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-544-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11902"><span style="display: inline-block; position: relative; width: 249px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11903"><span class="mi" id="MathJax-Span-11904" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-11905" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11906" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11907" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-11908" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11909" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-11910" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-11911" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11912" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-11913" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11914" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-11915" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-11916" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11917" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11918" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11919" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11920" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11921" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11922" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-11923" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11924" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11925" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11926" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-11927" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11928" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11929" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11930" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11931" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11932" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11933" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11934" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-544">wasInformedBy(id,a_2,a_1,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-545-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11935"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11936"><span class="mi" id="MathJax-Span-11937" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11938" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-545">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-546-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11939"><span style="display: inline-block; position: relative; width: 260px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11940"><span class="mi" id="MathJax-Span-11941" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-11942" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11943" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11944" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-11945" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11946" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11947" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11948" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11949" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11950" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-11951" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-11952" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11953" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11954" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11955" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11956" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11957" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11958" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-11959" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11960" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11961" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-11962" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11963" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11964" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-11965" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11966" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11967" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-11968" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11969" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-11970" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11971" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-11972" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11973" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-11974" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-546">wasStartedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-547-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11975"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11976"><span class="mi" id="MathJax-Span-11977" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11978" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-547">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-548-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-11979"><span style="display: inline-block; position: relative; width: 255px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-11980"><span class="mi" id="MathJax-Span-11981" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-11982" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-11983" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-11984" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-11985" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-11986" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-11987" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-11988" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-11989" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-11990" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-11991" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-11992" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-11993" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-11994" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-11995" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-11996" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-11997" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-11998" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-11999" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12000" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12001" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12002" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12003" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12004" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12005" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12006" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12007" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12008" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12009" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12010" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12011" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12012" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-548">wasEndedBy(id,a_2,e,a_1,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-549-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12013"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12014"><span class="mi" id="MathJax-Span-12015" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12016" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-549">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-550-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12017"><span style="display: inline-block; position: relative; width: 258px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12018"><span class="mi" id="MathJax-Span-12019" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12020" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12021" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12022" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-12023" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12024" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-12025" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12026" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-12027" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12028" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12029" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12030" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12031" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12032" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12033" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12034" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12035" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12036" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12037" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12038" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12039" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12040" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12041" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12042" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12043" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12044" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12045" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12046" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12047" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12048" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12049" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12050" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-550">wasInvalidatedBy(id,e,a,t,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-551-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12051"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12052"><span class="mi" id="MathJax-Span-12053" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12054" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-551">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-552-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12055"><span style="display: inline-block; position: relative; width: 326px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12056"><span class="mi" id="MathJax-Span-12057" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12058" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12059" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12060" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-12061" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12062" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12063" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12064" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-12065" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12066" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12067" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-12068" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12069" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-12070" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-12071" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12072" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12073" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12074" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12075" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12076" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12077" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12078" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12079" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12080" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12081" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12082" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12083" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12084" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12085" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12086" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-12087" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12088" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12089" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12090" style="font-family: STIXGeneral-Italic;">u</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12091" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12092" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12093" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12094" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12095" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12096" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12097" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12098" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-552">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 class="MathJax" id="MathJax-Element-553-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12099"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12100"><span class="mi" id="MathJax-Span-12101" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12102" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-553">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-554-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12103"><span style="display: inline-block; position: relative; width: 246px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12104"><span class="mi" id="MathJax-Span-12105" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12106" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12107" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12108" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-12109" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12110" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12111" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12112" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12113" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-12114" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-12115" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12116" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12117" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12118" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-12119" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-12120" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12122" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12123" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12124" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12125" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12126" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12127" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-12128" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12129" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12130" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12131" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12132" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12133" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12134" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-554">wasAttributedTo(id,e,ag,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-555-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12135"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12136"><span class="mi" id="MathJax-Span-12137" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12138" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-555">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-556-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12139"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12140"><span class="mi" id="MathJax-Span-12141" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12142" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12143" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12144" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-12145" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12146" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12147" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-12148" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-12149" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12150" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12151" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12152" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12153" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12154" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-12155" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12156" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12157" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-12158" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12159" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12160" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12161" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12162" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12163" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12164" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12165" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-12166" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12167" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-12168" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-12169" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12170" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12171" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12172" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12173" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12174" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12175" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-556">wasAssociatedWith(id,a,ag,pl,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-557-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12176"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12177"><span class="mi" id="MathJax-Span-12178" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12179" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-557">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-558-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12180"><span style="display: inline-block; position: relative; width: 302px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12181"><span class="mi" id="MathJax-Span-12182" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12183" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-12184" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12185" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12186" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12187" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-12188" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12189" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12190" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12191" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-12192" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12193" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-12194" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-12195" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-12196" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-12197" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12198" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12199" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12200" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12201" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-12202"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12203" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-12204" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12205" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12206" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-12207"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12208" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-12209" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12210" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12211" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12212" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12213" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12214" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12215" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12216" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12217" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12218" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-558">actedOnBehalfOf(id,ag_2,ag_1,a,attrs)</script> statement.</li>
+    <li>The identifier field <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-559-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12219"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12220"><span class="mi" id="MathJax-Span-12221" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12222" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-559">id</script> is a <span class="conditional">KEY</span> for the
+    <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-560-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12223"><span style="display: inline-block; position: relative; width: 261px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-12224"><span class="mi" id="MathJax-Span-12225" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12226" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12227" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12228" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-12229" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12230" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-12231" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-12232" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-12233" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12234" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12235" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-12236" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12237" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12238" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12239" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12240" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12241" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12242" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12243" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12244" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">o</span><span class="mn" id="MathJax-Span-12245" style="font-family: STIXGeneral-Regular;">2</span><span class="mo" id="MathJax-Span-12246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">o</span><span class="mn" id="MathJax-Span-12248" style="font-family: STIXGeneral-Regular;">1</span><span class="mo" id="MathJax-Span-12249" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12250" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12251" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12252" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12253" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12254" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12255" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-560">wasInfluencedBy(id,o2,o1,attrs)</script> statement.</li></ol>
   </div>
-<div class="constraint" number="24" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-561-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-561">\begin{array}[t]{l}
+<div class="constraint" number="24" id="unique-generation"><div class="ruleTitle"><a class="internalDFN" href="#unique-generation">Constraint 24 (unique-generation)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-561-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12256"><span style="display: inline-block; position: relative; width: 644px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.3px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12257"><span class="mtable" id="MathJax-Span-12258" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 638px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.3px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 638px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12259"><span class="mrow" id="MathJax-Span-12260"><span class="mi" id="MathJax-Span-12261" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12262" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-12263" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12264"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12265" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12266" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12267" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12268" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-12269" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12270"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12271" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12272" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12273" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12274" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12275" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12276" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12277" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12278" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12279" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12280" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12281" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12282" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12283" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12284" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12285" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12286" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12287" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12288" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12289" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12290"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12291" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12292" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12293" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12294" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12296" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12297" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12298"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12299" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12300" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12301" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-12302" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-12303"><span class="mrow" id="MathJax-Span-12304"><span class="mspace" id="MathJax-Span-12305" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-12306" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12307" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12308" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12309" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-12310" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12311" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12312" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12313" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12314" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12316" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12317" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12318" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12319" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12320" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12321" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-12322" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12323"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12324" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12325" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12326" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12327" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12328" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12329" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12330" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12331" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12332" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12333" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12334" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12335" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12336" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12337" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12338" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12339"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12340" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12341" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12342" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-12343" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-12344" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-12345" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12346" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12347" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-12348" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12349" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12350" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12351" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12352" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12353" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12354" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12355" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12356" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12357" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12358" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12359" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-12360" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12361"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12362" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12363" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12364" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12365" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12366" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12367" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12368" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12369" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12370" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12371" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12372" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12373" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12374" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12375" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12376" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12377"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12378" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12379" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12380" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(35.3px 19360px 56px -9px); top: 0.3px; left: 0px;"><span class="mtd" id="MathJax-Span-12381"><span class="mrow" id="MathJax-Span-12382"><span class="mspace" id="MathJax-Span-12383" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-12384" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-12385" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-12386" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12387"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12388" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12389" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12390" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-12391" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-12392" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-12393"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12394" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12395" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.8px; vertical-align: -54.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-561">\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)
@@ -2614,14 +2410,7 @@
 \quad\Rightarrow
 gen_1 = gen_2
 \end{array}</script></div>
-<div class="constraint" number="25" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-562-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-562">\begin{array}[t]{l}
+<div class="constraint" number="25" id="unique-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#unique-invalidation">Constraint 25 (unique-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-562-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12396"><span style="display: inline-block; position: relative; width: 650px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12397"><span class="mtable" id="MathJax-Span-12398" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 644px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.1px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 644px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12399"><span class="mrow" id="MathJax-Span-12400"><span class="mi" id="MathJax-Span-12401" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12402" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12403" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12404"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12405" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12406" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12407" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12408" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-12409" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12410"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12411" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12412" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12413" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12414" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12415" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12416" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12417" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12418" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12419" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12420" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12421" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12422" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12423" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12424" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12425" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12426" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12427" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12429" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12430"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12431" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12432" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12433" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12434" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12435" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12436" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12437" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12438"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12439" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12440" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12441" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-12442" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-12443"><span class="mrow" id="MathJax-Span-12444"><span class="mspace" id="MathJax-Span-12445" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-12446" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12447" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12448" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12449" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-12450" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12451" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-12452" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12453" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-12454" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12455" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12456" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12457" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12458" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12459" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12460" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12461" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12462" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12463" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12464" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12465"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12466" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12467" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12468" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12469" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12470" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12471" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12472" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12473" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12474" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12475" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12476" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12477" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12478" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12479" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12480" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12481"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12482" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12483" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12484" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-12485" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-12486" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-12487" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12488" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12489" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-12490" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12491" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-12492" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12493" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-12494" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12495" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12496" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12497" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12498" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12499" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12500" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12501" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12502" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12504" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12505"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12506" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12507" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12508" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12509" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12510" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12511" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12512" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12513" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12514" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12515" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12516" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12517" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12518" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12519" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12520" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12521"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12522" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12523" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12524" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 54.9px -9px); top: 1.2px; left: 0px;"><span class="mtd" id="MathJax-Span-12525"><span class="mrow" id="MathJax-Span-12526"><span class="mspace" id="MathJax-Span-12527" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-12528" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-12529" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-12530" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12531"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12532" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12533" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12534" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-12535" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-12536" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12537"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12538" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12539" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.6px; vertical-align: -55.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-562">\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)
@@ -2629,14 +2418,7 @@
 \quad\Rightarrow
 inv_1 = inv_2
 \end{array}</script></div>
-<div class="constraint" number="26" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-563-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-563">\begin{array}[t]{l}
+<div class="constraint" number="26" id="unique-wasStartedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasStartedBy">Constraint 26 (unique-wasStartedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-563-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12540"><span style="display: inline-block; position: relative; width: 679px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 96.3px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12541"><span class="mtable" id="MathJax-Span-12542" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 673px; height: 0px;"><span style="position: absolute; clip: rect(67.2px 19360px 137.3px -9px); top: -83px; left: 0px;"><span style="display: inline-block; position: relative; width: 673px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 54.1px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12543"><span class="mrow" id="MathJax-Span-12544"><span class="mi" id="MathJax-Span-12545" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12546" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12547" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12548" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12549" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12550"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12551" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12552" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12553" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12554" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-12555" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12556" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12557" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12558"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12559" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12560" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12561" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12562" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12563" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12564" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12565" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12566" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12567" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12568" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12569" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12570" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12571" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12572" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12573" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12574" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12575" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12576" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12577" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12578" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12579" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12580" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12581" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12582" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12583" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12584" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12585" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12586" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12587" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12588"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12589" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12590" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12591" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12592" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12593" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12594" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12595" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12596"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12597" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12598" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12599" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-12600" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-12601"><span class="mrow" id="MathJax-Span-12602"><span class="mspace" id="MathJax-Span-12603" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-12604" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12605" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12606" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12607" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-12608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12609" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12610" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12611" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12612" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12613" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12614" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12615" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12616" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12617" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12618" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12619" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12620" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12621"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12622" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12623" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12624" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12625" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12626" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12627" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12628" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12629" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12630" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12631" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12632" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12633" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12634" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12635" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12636" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12637" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12638" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12639" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12640" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12641" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12642" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12643"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12644" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12645" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12646" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-12647" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-12648" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-12649" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12650" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12651" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-12652" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12653" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12654" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12655" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12656" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12657" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12658" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12659" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12660" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12661" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12662" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12663" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12664" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12665"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12666" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12667" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12668" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12669" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12670" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12671" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12672" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12673" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12674" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12675" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12676" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12677" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12678" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12679" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12680" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12681" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12682" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12683" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12684" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12685" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12686" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12687"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12688" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12689" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12690" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(35.3px 19360px 54.9px -9px); top: -0.6px; left: 0px;"><span class="mtd" id="MathJax-Span-12691"><span class="mrow" id="MathJax-Span-12692"><span class="mspace" id="MathJax-Span-12693" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-12694" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-12695" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-12696" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12697" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12698" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12699"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12700" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12701" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12702" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-12703" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-12704" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12705" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12706" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12707"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12709" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 83px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 69.8px; vertical-align: -53.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-563">\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)
@@ -2644,14 +2426,7 @@
 \quad\Rightarrow
 start_1 = start_2
 \end{array}</script></div>
-<div class="constraint" number="27" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-564-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-564">\begin{array}[t]{l}
+<div class="constraint" number="27" id="unique-wasEndedBy"><div class="ruleTitle"><a class="internalDFN" href="#unique-wasEndedBy">Constraint 27 (unique-wasEndedBy)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-564-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12710"><span style="display: inline-block; position: relative; width: 655px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12711"><span class="mtable" id="MathJax-Span-12712" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 649px; height: 0px;"><span style="position: absolute; clip: rect(69.8px 19360px 142.9px -9px); top: -86px; left: 0px;"><span style="display: inline-block; position: relative; width: 649px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 54.1px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12713"><span class="mrow" id="MathJax-Span-12714"><span class="mi" id="MathJax-Span-12715" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12716" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12717" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12718"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12719" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12720" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12721" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12722" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-12723" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12724"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12725" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12726" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12727" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12728" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12729" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12730" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12731" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12732" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12733" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12734" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12735" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12736" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12737" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12738" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12739" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12740" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12741" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12742" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12743" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12744" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12745" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12746" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12747" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12748" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12749" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12750" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12751" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12752" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12753" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12754"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12755" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12756" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12757" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12758" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12759" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12760" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12761" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12762"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12763" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12764" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12765" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-12766" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-12767"><span class="mrow" id="MathJax-Span-12768"><span class="mspace" id="MathJax-Span-12769" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-12770" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-12771" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12772" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12773" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12774" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12775" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12776" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12777" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12778" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12779" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12780" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12781" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12782" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12783"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12784" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12785" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12786" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12787" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12788" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12789" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12790" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12791" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12792" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12793" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12794" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12795" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12796" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12797" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12798" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12799" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12800" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12801" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12802" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12803" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12804" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12805"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12806" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12807" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12808" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-12809" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-12810" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-12811" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12812" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12813" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12814" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12815" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12816" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12817" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12818" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12819" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12820" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12821" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12822" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12823"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12824" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12825" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12826" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12827" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-12828" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12829" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12830" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-12831" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12832" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12833" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12834" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12835" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">0</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12836" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12837" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12838" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12839" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12840" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12841" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12842" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12843" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12844" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12845"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12846" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12847" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12848" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54.9px -9px); top: 2px; left: 0px;"><span class="mtd" id="MathJax-Span-12849"><span class="mrow" id="MathJax-Span-12850"><span class="mspace" id="MathJax-Span-12851" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-12852" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-12853" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-12854" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12855"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12856" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12857" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12858" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-12859" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-12860" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-12861"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12862" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-12863" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 86px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.3px; vertical-align: -55.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-564">\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)
@@ -2659,14 +2434,7 @@
 \quad\Rightarrow
 end_1 = end_2
 \end{array}</script></div>
-<div class="constraint" number="28" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-565-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-565">\begin{array}[t]{l}
+<div class="constraint" number="28" id="unique-startTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-startTime">Constraint 28 (unique-startTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-565-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12864"><span style="display: inline-block; position: relative; width: 529px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 96.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12865"><span class="mtable" id="MathJax-Span-12866" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 523px; height: 0px;"><span style="position: absolute; clip: rect(67.2px 19360px 137.1px -9px); top: -83px; left: 0px;"><span style="display: inline-block; position: relative; width: 523px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12867"><span class="mrow" id="MathJax-Span-12868"><span class="mi" id="MathJax-Span-12869" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12870" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12871" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12872" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12873" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12874" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12875" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12876" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12877" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12878" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12879" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12880" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12881" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12882" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12883" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12884" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12885" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12886" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12887" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12888" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12889" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12890" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12891" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12892" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12893" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12894" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12895" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12896" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12897" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12898" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12899" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12900" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12903" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12904" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12905" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12906"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12907" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12908" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12909" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-12910" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-12911"><span class="mrow" id="MathJax-Span-12912"><span class="mspace" id="MathJax-Span-12913" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-12914" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12915" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-12916" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12917" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12918" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-12919" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-12920" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12921" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12922" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-12923"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12924" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12925" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12926" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12927" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12928" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12929" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12930" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12931" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12932" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12933" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12934" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12935" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12936" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12937" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12938" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12939" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-12940" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-12941" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-12942" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-12943" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12944" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12945" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-12946" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12947" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12948" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12949" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12951" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-12952" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-12953" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-12954" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-12955" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-12956" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12957" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-12958" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-12959" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12960" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12961" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12962" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12963" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12964" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12965" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-12966" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-12967" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12968" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-12969" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12970" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12971" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-12972" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-12973" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-12974" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12975" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-12976" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-12977"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12978" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-12979" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12980" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(35.3px 19360px 54.9px -9px); top: -0.8px; left: 0px;"><span class="mtd" id="MathJax-Span-12981"><span class="mrow" id="MathJax-Span-12982"><span class="mspace" id="MathJax-Span-12983" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-12984" style="font-family: STIXGeneral-Regular;">⇒</span><span class="msubsup" id="MathJax-Span-12985" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-12986" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-12987" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-12988" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-12989" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 83px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 69.6px; vertical-align: -53.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-565">\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)
@@ -2674,14 +2442,7 @@
 \quad\Rightarrow
 t_1 = t
 \end{array}</script></div>
-<div class="constraint" number="29" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-566-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-566">\begin{array}[t]{l}
+<div class="constraint" number="29" id="unique-endTime"><div class="ruleTitle"><a class="internalDFN" href="#unique-endTime">Constraint 29 (unique-endTime)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-566-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-12990"><span style="display: inline-block; position: relative; width: 517px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 96.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-12991"><span class="mtable" id="MathJax-Span-12992" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 511px; height: 0px;"><span style="position: absolute; clip: rect(67.8px 19360px 138.1px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 511px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-12993"><span class="mrow" id="MathJax-Span-12994"><span class="mi" id="MathJax-Span-12995" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-12996" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-12997" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-12998" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-12999" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13000" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13001" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13002" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13003" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13004" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13005" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13006" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13007" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13008" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13009" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13010" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13011" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13012" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13013" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13014" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13015" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13016" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13017" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13018" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-13019" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13020" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13021" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13023" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13024" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-13025" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13026" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13027" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13028" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13029" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13030"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13031" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13032" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13033" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13034" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13035"><span class="mrow" id="MathJax-Span-13036"><span class="mspace" id="MathJax-Span-13037" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13038" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13039" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-13040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13041" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-13042" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-13043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-13044" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13045" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13046" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-13047"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13048" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13049" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13050" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13051" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13053" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13054" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13055" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13056" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13057" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13058" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13059" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13060" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13061" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13062" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13063" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-13064" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13065" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13066" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13067" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13068" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13069" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13070" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13071" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13072" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13073" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13074" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13075" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13076" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13077" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13078" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13079" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13080" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13081" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13082" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13083" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13084" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13085" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-13086" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13087" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13088" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13089" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13090" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13091" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13092" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13093" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13094" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13095" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13096" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13097"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13098" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13099" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13100" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(35.3px 19360px 54.9px -9px); top: -0.8px; left: 0px;"><span class="mtd" id="MathJax-Span-13101"><span class="mrow" id="MathJax-Span-13102"><span class="mspace" id="MathJax-Span-13103" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13104" style="font-family: STIXGeneral-Regular;">⇒</span><span class="msubsup" id="MathJax-Span-13105" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13107" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13108" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-13109" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 69.6px; vertical-align: -53.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-566">\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)
@@ -2695,14 +2456,7 @@
 <h4><span class="secno">5.2.2 </span>Ordering constraints</h4>
 
 
-<div class="constraint" number="30" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-567-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-567">\begin{array}[t]{l}
+<div class="constraint" number="30" id="start-precedes-end"><div class="ruleTitle"><a class="internalDFN" href="#start-precedes-end">Constraint 30 (start-precedes-end)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-567-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13110"><span style="display: inline-block; position: relative; width: 650px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13111"><span class="mtable" id="MathJax-Span-13112" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 644px; height: 0px;"><span style="position: absolute; clip: rect(68.8px 19360px 140.8px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 644px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13113"><span class="mrow" id="MathJax-Span-13114"><span class="mi" id="MathJax-Span-13115" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13116" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13117" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13118" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13119" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13120" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13121" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13122" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-13123" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13124" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13125" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13126" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13127" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13128" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13129" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13130" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13131" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13132" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13133" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13134" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13135" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13136" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13137" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13138" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13139" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13140" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13141" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13142" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13143" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13144" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13145" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13146" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13147" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13148" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13149" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13150" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13151" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13152" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13153" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13154" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13155" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13156"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13157" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13158" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13159" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13160" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13161" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13162" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13163" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13164"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13165" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13166" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13167" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13168" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13169"><span class="mrow" id="MathJax-Span-13170"><span class="mspace" id="MathJax-Span-13171" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13172" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-13173" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13174" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13175" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-13176" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13177" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13178" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13179" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13180" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13181" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13182" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13183" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13184" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13185" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13186" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13187" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13188" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13189" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13190" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13191" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13192" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13193" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13194" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13195" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13196" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13197" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13198" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13199" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13200" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13201" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13202" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13203" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13204" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13205" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13206" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13207" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13208" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13209"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13210" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13211" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13212" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13213" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13214" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13215" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13216" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13217" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13218" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13219" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13220" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13221" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13222" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13223" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13224" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13225" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13226" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13227" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13228" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13229" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13230" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13231" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13232" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13233" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13234" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13235" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13236" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13237" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13238" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13239" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13240" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13241" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13242" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13243" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13244" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13245" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13246" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13247"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13248" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13249" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13250" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-13251"><span class="mrow" id="MathJax-Span-13252"><span class="mspace" id="MathJax-Span-13253" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13254" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-13255" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-13256" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13257" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13258" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13259" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13260" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-13261" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-13262" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13263" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-567">\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)
@@ -2710,14 +2464,7 @@
 \quad\Rightarrow
 start \preceq end
 \end{array}</script></div>
-<div class="constraint" number="31" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-568-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-568">\begin{array}[t]{l}
+<div class="constraint" number="31" id="start-start-ordering"><div class="ruleTitle"><a class="internalDFN" href="#start-start-ordering">Constraint 31 (start-start-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-568-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13264"><span style="display: inline-block; position: relative; width: 679px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13265"><span class="mtable" id="MathJax-Span-13266" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 673px; height: 0px;"><span style="position: absolute; clip: rect(68.2px 19360px 139.2px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 673px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13267"><span class="mrow" id="MathJax-Span-13268"><span class="mi" id="MathJax-Span-13269" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13270" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13271" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13272" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13273" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13274"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13275" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13276" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13277" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13278" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-13279" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13280" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13281" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13282"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13283" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13284" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13285" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13286" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13287" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13288" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13289" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13290" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13291" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13292" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13293" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13294" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13295" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13296" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13297" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13298" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13299" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13300" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13301" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13302" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13303" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13304" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13305" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13306" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13307" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13308" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13309" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13310" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13311" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13312" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13313" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13314" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13315" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13316"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13317" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13318" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13319" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13320" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13321" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13322" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13323" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13324"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13325" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13326" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13327" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13328" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13329"><span class="mrow" id="MathJax-Span-13330"><span class="mspace" id="MathJax-Span-13331" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13332" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-13333" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13334" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13335" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-13336" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13337" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13338" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13339" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13340" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13341" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13342" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13343" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13344" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13345" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13346" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13347" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13348" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13349"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13350" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13351" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13352" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13353" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13354" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13355" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13356" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13357" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13358" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13359" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13360" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13361" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13362" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13363" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13364" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13365" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13366" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13367" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13368" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13369" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13370" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13371"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13372" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13373" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13374" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13375" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13376" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13377" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13378" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13379" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-13380" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13381" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13382" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13383" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13384" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13385" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13386" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13387" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13388" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13389" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13390" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13391" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13392" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13393"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13394" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13395" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13396" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13397" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13398" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13399" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13400" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13401" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13402" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13403" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13404" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13405" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13406" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13407" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13408" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13409" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13410" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13411" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13412" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13413" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13414" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13415"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13416" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13417" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13418" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 54.9px -9px); top: 0.3px; left: 0px;"><span class="mtd" id="MathJax-Span-13419"><span class="mrow" id="MathJax-Span-13420"><span class="mspace" id="MathJax-Span-13421" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13422" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-13423" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-13424" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13425" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13426" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13427"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13429" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13430" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-13431" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-13432" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13433" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13434" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13435"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13436" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13437" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.7px; vertical-align: -54.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-568">\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)
@@ -2725,14 +2472,7 @@
 \quad\Rightarrow
 start_1 \preceq start_2
 \end{array}</script></div>
-<div class="constraint" number="32" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-569-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-569">\begin{array}[t]{l}
+<div class="constraint" number="32" id="end-end-ordering"><div class="ruleTitle"><a class="internalDFN" href="#end-end-ordering">Constraint 32 (end-end-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-569-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13438"><span style="display: inline-block; position: relative; width: 655px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13439"><span class="mtable" id="MathJax-Span-13440" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 649px; height: 0px;"><span style="position: absolute; clip: rect(69.8px 19360px 142.7px -9px); top: -86px; left: 0px;"><span style="display: inline-block; position: relative; width: 649px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13441"><span class="mrow" id="MathJax-Span-13442"><span class="mi" id="MathJax-Span-13443" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13444" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13445" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13446"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13447" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13448" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13449" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13450" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-13451" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13452"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13453" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13454" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13455" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13456" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13457" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13458" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13459" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13460" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13461" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13462" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13463" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13464" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13465" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13466" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13467" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13468" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13469" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13470" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13471" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13472" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13473" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13474" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13475" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13476" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13477" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13478" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13479" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13480" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13483" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13485" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13486"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13487" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13488" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13489" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13490" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13491" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13492" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13493" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13494"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13495" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13496" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13497" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13498" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13499"><span class="mrow" id="MathJax-Span-13500"><span class="mspace" id="MathJax-Span-13501" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13502" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-13503" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13504" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13505" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13506" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13507" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13508" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13509" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13510" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13511" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13512" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13513" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13514" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13515"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13516" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13517" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13518" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13519" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13520" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13521" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13522" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13523" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13524" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13525" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13526" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13527" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13528" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13529" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13530" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13531" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13532" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13533" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13534" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13535" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13536" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13537"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13538" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13539" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13540" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13541" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13542" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13543" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13544" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13545" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13546" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13547" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13548" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13549" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13550" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13551" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13552" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13553" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13554" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13555"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13556" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13557" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13558" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13559" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13560" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13561" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13562" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13563" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13564" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13565" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13566" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13567" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13568" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13569" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13570" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13571" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13572" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13573" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13574" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13575" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13576" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13577"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13578" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13579" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13580" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54.9px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-13581"><span class="mrow" id="MathJax-Span-13582"><span class="mspace" id="MathJax-Span-13583" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13584" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-13585" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-13586" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13587"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13588" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13589" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13590" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-13591" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-13592" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-13593"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13594" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-13595" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 86px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-569">\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)
@@ -2740,28 +2480,14 @@
 \quad\Rightarrow
 end_1 \preceq end_2
 \end{array}</script></div>
-<div class="constraint" number="33" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="33" id="usage-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#usage-within-activity">Constraint 33 (usage-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-570-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13596"><span style="display: inline-block; position: relative; width: 554px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13597"><span class="mtable" id="MathJax-Span-13598" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 548px; height: 0px;"><span style="position: absolute; clip: rect(67.2px 19360px 137.3px -9px); top: -83px; left: 0px;"><span style="display: inline-block; position: relative; width: 548px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13599"><span class="mrow" id="MathJax-Span-13600"><span class="mi" id="MathJax-Span-13601" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13602" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13603" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13604" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13605" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13606" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13607" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13608" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-13609" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13610" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-13611" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13612" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13613" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13614" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13615" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13616" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13617" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13618" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13619" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13620" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13621" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13622" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13623" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13624" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13625" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13626" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13627" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13628" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13629" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13630" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13631" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13632" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13633" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13634" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13635" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13636" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13637" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13638"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13639" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13640" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13641" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13642" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13643" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13644" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13645" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13646"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13647" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13648" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13649" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13650" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13651"><span class="mrow" id="MathJax-Span-13652"><span class="mspace" id="MathJax-Span-13653" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13654" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-13655" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13656" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13657" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-13658" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13659" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13660" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13661" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13662" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13663" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13664" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13665" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13666" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13667" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13668" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13669" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13670" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13671" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13672" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13673" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13674" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13675" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13676" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13677" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13678" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13679" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13680" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13681" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13682" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13683" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13684" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13685" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13686" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13687" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13688" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13689" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13690" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13691"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13692" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13693" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13694" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13695" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13696" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-13697" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13698" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13699" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13700" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13701" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-13702" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13703" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-13704" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13705" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13706" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13707" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13708" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13709" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13710" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13711" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13712" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13713" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13714" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13715" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13716" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13717" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13718" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13719"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13720" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13721" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13722" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 54px -9px); top: 0.3px; left: 0px;"><span class="mtd" id="MathJax-Span-13723"><span class="mrow" id="MathJax-Span-13724"><span class="mspace" id="MathJax-Span-13725" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13726" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-13727" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-13728" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13729" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13730" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13731" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13732" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-13733" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-13734" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13735" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 83px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.7px; vertical-align: -54.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-570">\begin{array}[t]{l}
 \forall start,use,a,e_1,e_2,a_1,t_1,t_2,attrs_1,attrs_2.~
 \\
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 \\
 \quad\Rightarrow
 start \preceq use
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-\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
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-\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-571-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-571">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-571-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13736"><span style="display: inline-block; position: relative; width: 542px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13737"><span class="mtable" id="MathJax-Span-13738" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 536px; height: 0px;"><span style="position: absolute; clip: rect(68.8px 19360px 140.8px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 536px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13739"><span class="mrow" id="MathJax-Span-13740"><span class="mi" id="MathJax-Span-13741" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13742" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-13743" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13744" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-13745" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13746" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-13747" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13748" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13749" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13750" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13751" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13752" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13753" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13754" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13755" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13756" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13757" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13758" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13759" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13760" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13761" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13762" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13763" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13764" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13765" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13766" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13767" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13768" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13769" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13770" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13771" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13772" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13773" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13774" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13775" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13776"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13777" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13778" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13779" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13780" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13781" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13782" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13783" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13784"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13785" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13786" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13787" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13788" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-13789"><span class="mrow" id="MathJax-Span-13790"><span class="mspace" id="MathJax-Span-13791" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13792" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-13793" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13794" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13795" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13796" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13797" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-13798" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13799" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-13800" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13801" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13802" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13803" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13804" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13805" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13806" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13807" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13808" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13809" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13810" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13811" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13812" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13813" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13814" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13815"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13816" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13817" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13818" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13819" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13820" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13822" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13823" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13825" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13826" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13827" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13828" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13829" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13830" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13831" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13832" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13833" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-13834" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13835" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13836" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13837" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13838" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13839" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13840" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13841" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13842" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13843" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13844" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13845" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13846" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13847" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13848" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13849" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13850" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13851" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13852" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13853"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13854" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13855" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13856" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-13857"><span class="mrow" id="MathJax-Span-13858"><span class="mspace" id="MathJax-Span-13859" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-13860" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-13861" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-13862" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13863" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-13864" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-13865" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-13866" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13867" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-571">\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)
@@ -2769,28 +2495,14 @@
 \quad\Rightarrow
 use \preceq end
 \end{array}</script></li></ol></div>
-<div class="constraint" number="34" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="34" id="generation-within-activity"><div class="ruleTitle"><a class="internalDFN" href="#generation-within-activity">Constraint 34 (generation-within-activity)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-572-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-13868"><span style="display: inline-block; position: relative; width: 653px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-13869"><span class="mtable" id="MathJax-Span-13870" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 647px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 647px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-13871"><span class="mrow" id="MathJax-Span-13872"><span class="mi" id="MathJax-Span-13873" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-13874" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13875" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13876" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13877" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13878" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13879" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13880" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-13881" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13882" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-13883" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13884" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13885" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13886" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13887" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13888" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13889" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13890" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13891" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13892" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13893" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13894" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13895" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13896" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13897" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13898" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13899" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13900" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13901" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13902" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13903" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13904" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13905" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13906" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13907" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13908" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13909" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13910"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13911" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13912" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13913" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13914" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13915" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13916" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13917" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13918"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13919" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13920" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13921" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-13922" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-13923"><span class="mrow" id="MathJax-Span-13924"><span class="mspace" id="MathJax-Span-13925" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-13926" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-13927" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13928" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13929" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-13930" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13931" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13932" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13933" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13934" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13935" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13936" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13937" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13938" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13939" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13940" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13941" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13942" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13943" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-13944" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13945" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13946" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13947" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13948" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13949" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13950" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13951" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13952" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-13953" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13954" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13955" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13956" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13957" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13958" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13959" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13960" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13961" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13962" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-13963"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13964" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-13965" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13966" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-13967" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-13968" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-13969" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13970" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-13971" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-13972" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13973" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-13974" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13975" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-13976" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-13977" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13978" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13979" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-13980" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-13981" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-13982" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-13983" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-13984" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-13985" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-13986" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13987" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13988" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-13989" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-13992" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-13993" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-13994" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-13995" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-13996" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-13997" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-13998" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-13999" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14000" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14001"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14002" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14003" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14004" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-14005"><span class="mrow" id="MathJax-Span-14006"><span class="mspace" id="MathJax-Span-14007" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14008" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14009" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-14010" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14011" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14012" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14013" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-14014" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14015" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14016" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14017" style="font-family: STIXGeneral-Italic;">n</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-572">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-572-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-572">\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
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-\end{array}</script></li><li><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-573-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-573">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-573-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14018"><span style="display: inline-block; position: relative; width: 615px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14019"><span class="mtable" id="MathJax-Span-14020" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 609px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 609px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14021"><span class="mrow" id="MathJax-Span-14022"><span class="mi" id="MathJax-Span-14023" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14024" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14025" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14026" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14027" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14028" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-14029" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14030" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14031" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14032" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14033" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14034" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14035" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14036" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14037" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14038" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-14039" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14040" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14041" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14042" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14043" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14044" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-14045" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14046" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14047" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14048" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14049" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14050" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14051" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14053" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; 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clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14061" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14062" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14063" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14064" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-14065"><span class="mrow" id="MathJax-Span-14066"><span class="mspace" id="MathJax-Span-14067" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14068" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14069" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14070" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14071" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-14072" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14073" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14074" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14075" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14076" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14077" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-14116" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14117" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14118" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14119" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14120" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14121" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14122" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14123" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14124" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14125" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14126" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14127" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14128" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14129" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14130" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14131" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14132" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14133"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14134" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14135" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14136" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-14137"><span class="mrow" id="MathJax-Span-14138"><span class="mspace" id="MathJax-Span-14139" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14140" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14141" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14143" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14144" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14145" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-14146" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14147" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-573">\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)
@@ -2798,14 +2510,7 @@
 \quad\Rightarrow
 gen \preceq end
 \end{array}</script></li></ol></div>
-<div class="constraint" number="35" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-574-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-574">\begin{array}[t]{l}
+<div class="constraint" number="35" id="wasInformedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasInformedBy-ordering">Constraint 35 (wasInformedBy-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-574-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14148"><span style="display: inline-block; position: relative; width: 934px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 104.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14149"><span class="mtable" id="MathJax-Span-14150" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 928px; height: 0px;"><span style="position: absolute; clip: rect(75px 19360px 153.8px -9px); top: -92px; left: 0px;"><span style="display: inline-block; position: relative; width: 928px; height: 0px;"><span style="position: absolute; clip: rect(31px 19360px 57.1px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14151"><span class="mrow" id="MathJax-Span-14152"><span class="mi" id="MathJax-Span-14153" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14154" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14155" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14156" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14157" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-14158" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14159" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14160" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14161" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-14162" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14163" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-14164" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14165" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14166" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14167" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14168" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14169" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14170" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14171" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14172" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.3px 19360px 44.6px -8.4px); top: -48.3px; left: 10px;"><span class="mo" id="MathJax-Span-14173" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span><span style="position: absolute; clip: rect(29.7px 19360px 45px -7.5px); top: -35.9px; left: 10px;"><span class="mn" id="MathJax-Span-14174" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14175" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14176" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14177" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14178" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14179" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14180" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14181" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.3px 19360px 44.6px -8.4px); top: -48.3px; left: 10px;"><span class="mo" id="MathJax-Span-14182" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span><span style="position: absolute; clip: rect(29.7px 19360px 45px -8.6px); top: -35.9px; left: 10px;"><span class="mn" id="MathJax-Span-14183" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14184" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14185" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14186" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14187" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14188" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14189" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14190" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14191" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14192" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14193" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14194" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14195" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14196" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14197" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14198" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14199" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14200" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14201" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14202" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14203" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14204" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14205" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-14206" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14207" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14208" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14209" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14210" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14211"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14212" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14213" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14214" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14215" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14216" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14217" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14218" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14219"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14220" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14221" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14222" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14223" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31px 19360px 57.1px -9px); top: -19.2px; left: 0px;"><span class="mtd" id="MathJax-Span-14224"><span class="mrow" id="MathJax-Span-14225"><span class="mspace" id="MathJax-Span-14226" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14227" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14228" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14229" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14230" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-14231" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14232" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-14233" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-14234" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14235" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-14236" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14237" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14238" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14239" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14240" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14241" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14242" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14243" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14244" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14245" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14246" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14247" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14248" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14249" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14250" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14251" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14252" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14253" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14254" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14255" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14256" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-14257" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14258" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14259" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-14260" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14261" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14262" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-14263" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14264" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14265" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14266" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14267" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14268" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14269" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14270" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14271" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14272" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14273" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14274" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14275" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14276" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-14277" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14278" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14279" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14280" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14281" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14282" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14283" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14284" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14285" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14286" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14287" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.3px 19360px 44.6px -8.4px); top: -48.3px; left: 10px;"><span class="mo" id="MathJax-Span-14288" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span><span style="position: absolute; clip: rect(29.7px 19360px 45px -7.5px); top: -35.9px; left: 10px;"><span class="mn" id="MathJax-Span-14289" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14290" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14291" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14292" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14293" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14294" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14295" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14296" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14297" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14298" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14299"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14300" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14301" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14302" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14303" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14304" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-14305" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14306" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14307" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14308" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14309" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14310" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14311" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14312" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14313" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14314" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14315" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14316" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14317" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14318" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14319" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14320" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14321" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14322" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14323" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14324" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14325" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14326" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14327" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14328" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.3px 19360px 44.6px -8.4px); top: -48.3px; left: 10px;"><span class="mo" id="MathJax-Span-14329" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span><span style="position: absolute; clip: rect(29.7px 19360px 45px -8.6px); top: -35.9px; left: 10px;"><span class="mn" id="MathJax-Span-14330" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14331" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14332" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14333" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14334" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14335" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14336" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14337" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14338" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14339" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14340"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14341" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14342" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14343" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54px -9px); top: 7.8px; left: 0px;"><span class="mtd" id="MathJax-Span-14344"><span class="mrow" id="MathJax-Span-14345"><span class="mspace" id="MathJax-Span-14346" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14347" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14348" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-14349" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14350" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14351" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14352" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-14353" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14354" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-14355" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14356" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 92px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 78.2px; vertical-align: -61.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-574">\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)
@@ -2813,14 +2518,7 @@
 \quad\Rightarrow
 start \preceq end
 \end{array}</script></div>
-<div class="constraint" number="36" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-575-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-575">\begin{array}[t]{l}
+<div class="constraint" number="36" id="generation-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-invalidation">Constraint 36 (generation-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-575-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14357"><span style="display: inline-block; position: relative; width: 647px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.3px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14358"><span class="mtable" id="MathJax-Span-14359" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 641px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 145.3px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 641px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14360"><span class="mrow" id="MathJax-Span-14361"><span class="mi" id="MathJax-Span-14362" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14363" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14364" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14365" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14366" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14367" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-14368" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14369" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-14370" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14371" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14372" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14373" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14374" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14375" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14376" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14377" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14378" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14379" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14380" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14381" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14382" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14383" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14384" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14385" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14386" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14387" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14388" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14389" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14390" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14391" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14392" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14393"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14394" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14395" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14396" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14397" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14398" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14399" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14400" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14401"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14402" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14403" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14404" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14405" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-14406"><span class="mrow" id="MathJax-Span-14407"><span class="mspace" id="MathJax-Span-14408" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14409" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14410" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14411" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14412" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-14413" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14414" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14415" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14416" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14417" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14418" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14419" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14420" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14421" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14422" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14423" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14424" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14425" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14426" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14427" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14428" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14429" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14430" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14431" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14432" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14433" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14434" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14435" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14436" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14437" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14438" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14439" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14441" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14442"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14443" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14444" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14445" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14446" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14447" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-14448" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14449" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14450" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-14451" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14452" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-14453" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14454" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-14455" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14456" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14457" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14458" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14459" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14460" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14461" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14462" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14463" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14464" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14465" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14466" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-14467" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14468" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14469" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14470" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14471" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14472" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14473" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14474" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14475" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14476" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14477" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14478" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14479" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14480" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14481" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14482"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14483" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14484" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14485" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 56px -9px); top: 2.3px; left: 0px;"><span class="mtd" id="MathJax-Span-14486"><span class="mrow" id="MathJax-Span-14487"><span class="mspace" id="MathJax-Span-14488" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14489" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14490" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14491" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14492" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14493" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14494" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-14495" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14496" style="font-family: STIXGeneral-Italic;">v</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.8px; vertical-align: -56.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-575">\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)
@@ -2828,14 +2526,7 @@
 \quad\Rightarrow
 gen \preceq inv
 \end{array}</script></div>
-<div class="constraint" number="37" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-576-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-576">\begin{array}[t]{l}
+<div class="constraint" number="37" id="generation-precedes-usage"><div class="ruleTitle"><a class="internalDFN" href="#generation-precedes-usage">Constraint 37 (generation-precedes-usage)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-576-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14497"><span style="display: inline-block; position: relative; width: 545px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14498"><span class="mtable" id="MathJax-Span-14499" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 539px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 539px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14500"><span class="mrow" id="MathJax-Span-14501"><span class="mi" id="MathJax-Span-14502" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14503" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14504" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14505" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14506" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14507" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-14508" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14509" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-14510" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14511" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14512" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14513" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14514" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14515" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14516" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14517" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14518" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14519" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14520" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14521" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14522" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14523" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14524" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14525" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14526" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14527" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14528" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14529" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14530" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14531" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14532" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14533"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14534" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14535" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14536" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14537" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14538" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14539" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14540" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14541"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14542" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14543" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14544" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14545" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-14546"><span class="mrow" id="MathJax-Span-14547"><span class="mspace" id="MathJax-Span-14548" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14549" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14550" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14551" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14552" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-14553" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14554" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14555" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14556" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14557" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14558" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14559" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14560" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14561" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14562" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14563" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14564" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14565" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14566" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14567" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14568" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14569" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14570" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14571" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14572" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14573" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14574" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14575" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14576" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14577" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14578" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14579" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14580" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14581" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14582"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14583" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14584" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14585" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14586" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14587" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-14588" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14589" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14590" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14591" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14592" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-14593" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14594" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-14595" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14596" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14597" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14598" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14599" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14600" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14601" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14602" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14603" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14604" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14605" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14606" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14607" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14609" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14610"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14611" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14612" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14613" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-14614"><span class="mrow" id="MathJax-Span-14615"><span class="mspace" id="MathJax-Span-14616" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14617" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14618" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14619" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14620" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-14621" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14622" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-14623" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14624" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-576">\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)
@@ -2843,14 +2534,7 @@
 \quad\Rightarrow
 gen \preceq use
 \end{array}</script></div>
-<div class="constraint" number="38" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-577-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-577">\begin{array}[t]{l}
+<div class="constraint" number="38" id="usage-precedes-invalidation"><div class="ruleTitle"><a class="internalDFN" href="#usage-precedes-invalidation">Constraint 38 (usage-precedes-invalidation)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-577-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14625"><span style="display: inline-block; position: relative; width: 548px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14626"><span class="mtable" id="MathJax-Span-14627" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 542px; height: 0px;"><span style="position: absolute; clip: rect(68.2px 19360px 139.2px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 542px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14628"><span class="mrow" id="MathJax-Span-14629"><span class="mi" id="MathJax-Span-14630" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14631" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-14632" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14633" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-14634" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14635" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-14636" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14637" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-14638" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14639" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14640" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14641" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14642" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14643" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14644" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14645" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14646" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14647" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14648" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14649" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14650" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14651" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14652" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14653" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14654" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14655" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14656" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14657" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14658" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14660" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14661"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14662" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14663" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14664" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14665" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14666" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14667" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14668" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14669"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14670" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14671" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14672" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14673" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-14674"><span class="mrow" id="MathJax-Span-14675"><span class="mspace" id="MathJax-Span-14676" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14677" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-14678" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14679" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14680" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-14681" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14682" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-14683" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14684" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-14685" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14686" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14687" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14688" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14689" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14690" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14691" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14692" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14693" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14694" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14695" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14696" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14697" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14698" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14699" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14700"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14701" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14702" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14703" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14704" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14705" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-14706" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14707" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14708" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-14709" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14710" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-14711" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14712" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-14713" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14714" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14715" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14716" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14717" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14718" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14719" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14720" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14721" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14722" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14723" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14724" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-14725" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14726" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14727" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14728" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14729" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14730" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14731" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14732" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14733" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14734" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14735" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14736" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14737" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14738" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14739" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14740"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14741" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14742" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14743" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 54px -9px); top: 1.2px; left: 0px;"><span class="mtd" id="MathJax-Span-14744"><span class="mrow" id="MathJax-Span-14745"><span class="mspace" id="MathJax-Span-14746" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14747" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14748" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-14749" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14750" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-14751" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14752" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-14753" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14754" style="font-family: STIXGeneral-Italic;">v</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.6px; vertical-align: -55.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-577">\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)
@@ -2858,14 +2542,7 @@
 \quad\Rightarrow
 use \preceq inv
 \end{array}</script></div>
-<div class="constraint" number="39" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-578-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-578">\begin{array}[t]{l}
+<div class="constraint" number="39" id="generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#generation-generation-ordering">Constraint 39 (generation-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-578-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14755"><span style="display: inline-block; position: relative; width: 661px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14756"><span class="mtable" id="MathJax-Span-14757" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 655px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 655px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14758"><span class="mrow" id="MathJax-Span-14759"><span class="mi" id="MathJax-Span-14760" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14761" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14762" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14763"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14764" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14765" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14766" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14767" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-14768" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14769"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14770" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14771" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14772" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14773" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14774" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14775" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14776" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14777" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14778" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14779" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14780" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14781" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14782" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14783" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14784" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14785" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14786" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14787" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14788" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14789" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14790" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14791" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14792" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14793" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14794" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14795"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14796" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14797" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14798" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14799" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14801" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14802" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14803"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14804" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14805" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14806" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14807" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-14808"><span class="mrow" id="MathJax-Span-14809"><span class="mspace" id="MathJax-Span-14810" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14811" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14812" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14813" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14814" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-14815" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14816" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14817" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14818" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14819" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14820" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14821" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14822" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14823" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14824" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14825" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14826" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14827" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14828"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14829" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14830" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14831" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14832" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14833" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14834" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14835" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14836" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14837" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14838" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14839" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14840" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14841" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14842" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14843" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14845" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14846"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14847" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14848" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14849" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-14850" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-14851" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-14852" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14853" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14854" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-14855" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14856" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14857" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14858" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-14859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14860" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14861" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14862" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14863" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14864" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14865" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14866" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-14867" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14868"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14869" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14870" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14871" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14872" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14873" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14874" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14875" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14876" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14877" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14878" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14879" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14880" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14881" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14882" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14883" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14884" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14885" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14886"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14887" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14888" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14889" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-14890"><span class="mrow" id="MathJax-Span-14891"><span class="mspace" id="MathJax-Span-14892" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-14893" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-14894" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14895" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14896"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14897" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14898" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14899" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-14900" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-14901" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-14902"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14903" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14904" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-578">\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)
@@ -2873,14 +2550,7 @@
 \quad\Rightarrow
 gen_1 \preceq gen_2
 \end{array}</script></div>
-<div class="constraint" number="40" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-579-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-579">\begin{array}[t]{l}
+<div class="constraint" number="40" id="invalidation-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#invalidation-invalidation-ordering">Constraint 40 (invalidation-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-579-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-14905"><span style="display: inline-block; position: relative; width: 667px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-14906"><span class="mtable" id="MathJax-Span-14907" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 661px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.1px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 661px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-14908"><span class="mrow" id="MathJax-Span-14909"><span class="mi" id="MathJax-Span-14910" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-14911" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14912" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-14913"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14914" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14915" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14916" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14917" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-14918" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-14919"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14920" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14921" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14922" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14923" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14924" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14925" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14926" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14927" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14928" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14929" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14930" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14931" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14932" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14933" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14934" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14935" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14936" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14937" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14939" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14940" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14941" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14942" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14943" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14944" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14945"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14946" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14947" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14948" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14949" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14950" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14951" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14952" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14953"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14954" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-14955" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14956" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-14957" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-14958"><span class="mrow" id="MathJax-Span-14959"><span class="mspace" id="MathJax-Span-14960" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-14961" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-14962" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14963" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-14964" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-14965" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-14966" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-14967" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14968" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-14969" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14970" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14971" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-14972" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14973" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-14974" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-14975" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-14976" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-14977" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-14978" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-14979" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-14980"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14981" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-14982" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14983" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14984" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-14985" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14986" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14987" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-14988" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14989" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-14990" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14991" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-14992" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-14993" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-14994" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-14995" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14996" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-14997" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-14998"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-14999" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15000" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15001" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15002" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15003" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15004" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15005" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15006" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-15007" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15008" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-15009" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15010" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15011" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15012" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15013" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15014" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15015" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15016" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15017" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15018" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15019" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15020" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15021" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-15022"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15023" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15024" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15025" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15026" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15027" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15028" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15029" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15030" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15031" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15032" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15033" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15034" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15035" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15036" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15037" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15038" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15039" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15040"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15041" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15042" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15043" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 54.9px -9px); top: 1.2px; left: 0px;"><span class="mtd" id="MathJax-Span-15044"><span class="mrow" id="MathJax-Span-15045"><span class="mspace" id="MathJax-Span-15046" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15047" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15048" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-15049" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-15050"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15051" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15052" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15053" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-15054" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-15055" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-15056"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15057" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15058" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.6px; vertical-align: -55.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-579">\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)
@@ -2888,14 +2558,7 @@
 \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 class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-580-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-580">a</script>,<span class="MathJax_Preview">gen_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-581-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-581">gen_2</script>, or <span class="MathJax_Preview">use_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-582-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-582">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-583-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-583">\begin{array}[t]{l}
+<div class="constraint" number="41" id="derivation-usage-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-usage-generation-ordering">Constraint 41 (derivation-usage-generation-ordering)</a></div><p>In this constraint, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-580-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15059"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15060"><span class="mi" id="MathJax-Span-15061" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-580">a</script>,<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-581-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15062"><span style="display: inline-block; position: relative; width: 37px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15063"><span class="mi" id="MathJax-Span-15064" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15065" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15066"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15067" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15068" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-581">gen_2</script>, or <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-582-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15069"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 53.9px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15070"><span class="mi" id="MathJax-Span-15071" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-15072" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-15073"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15074" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15075" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-582">use_1</script> must not be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-583-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15076"><span style="display: inline-block; position: relative; width: 755px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15077"><span class="mtable" id="MathJax-Span-15078" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 749px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 749px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15079"><span class="mrow" id="MathJax-Span-15080"><span class="mi" id="MathJax-Span-15081" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15082" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15083" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15084" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15085" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15086" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15087" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15088" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15089" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15090" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15091" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15092" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15093" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15094" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-15095" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15096"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15097" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15098" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15099" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15100" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-15101" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-15102"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15103" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15104" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15105" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15106" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15107" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15108" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15109" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15110" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-15111" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15112" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-15113"><span class="mrow" id="MathJax-Span-15114"><span class="mspace" id="MathJax-Span-15115" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15116" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15117" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-15118" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15119" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-15120" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-15121" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15122" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-15123" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15124" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-15125" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15126" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15127" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-15128" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-15129" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15130" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-15131" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-15132" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15133" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-15134" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15135" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15136" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15137"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15138" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15139" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15140" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15141" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15142" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-15143" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-15144" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15145" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-15146" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-15147" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15148" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-15149" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15150" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-15151" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-15152"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15153" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15154" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15155" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15156" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15157" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15158" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15159" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15160" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-15161" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15162" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15164" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-15165" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15166" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15167" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-15168" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15169" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-15170" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-15171" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15172" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15173" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15174" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15175" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15176" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15177" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15178" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15179" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15180" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15181" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15182" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15183" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15184" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-15185" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15186"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15187" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15188" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15189" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15190" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mi" id="MathJax-Span-15191" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-15192"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15193" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15194" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15195" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15196" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15197" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15198" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15199" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15200" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-15201" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-15202"><span class="mrow" id="MathJax-Span-15203"><span class="mspace" id="MathJax-Span-15204" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15205" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15206" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-15207" style="font-family: STIXGeneral-Italic;">s</span><span class="msubsup" id="MathJax-Span-15208"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15209" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15210" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15211" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-15212" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-15213" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15214"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15215" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15216" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-583">\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)
@@ -2903,14 +2566,7 @@
 \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 class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-584-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-584">a</script>,<span class="MathJax_Preview">g</span><span class="MathJax MathJax_Processing" id="MathJax-Element-585-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-585">g</script>, or <span class="MathJax_Preview">u</span><span class="MathJax MathJax_Processing" id="MathJax-Element-586-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-586">u</script> may be placeholders -.</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-587-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-587">\begin{array}[t]{l}
+<div class="constraint" number="42" id="derivation-generation-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#derivation-generation-generation-ordering">Constraint 42 (derivation-generation-generation-ordering)</a></div><p>In this constraint, any of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-584-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15217"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15218"><span class="mi" id="MathJax-Span-15219" style="font-family: STIXGeneral-Italic;">a</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-584">a</script>,<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-585-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15220"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15221"><span class="mi" id="MathJax-Span-15222" style="font-family: STIXGeneral-Italic;">g</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-585">g</script>, or <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-586-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15223"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-15224"><span class="mi" id="MathJax-Span-15225" style="font-family: STIXGeneral-Italic;">u</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-586">u</script> may be placeholders -.</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-587-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15226"><span style="display: inline-block; position: relative; width: 1000px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.3px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15227"><span class="mtable" id="MathJax-Span-15228" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 994px; height: 0px;"><span style="position: absolute; clip: rect(69.8px 19360px 142.3px -9px); top: -86px; left: 0px;"><span style="display: inline-block; position: relative; width: 994px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15229"><span class="mrow" id="MathJax-Span-15230"><span class="mi" id="MathJax-Span-15231" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15232" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15233" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15234" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-15235" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15236"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15237" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15238" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15239" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15240" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-15241" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15242"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15243" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15244" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15245" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15246" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15247" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15248" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15249" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15250" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15251" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15252" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15253" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15254" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15255" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15256" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15257" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15258" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15259" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15260" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15261" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15262" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15263" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15264" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-15265" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15266" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-15267" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15268" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15269" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15270" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15271" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15272" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15273" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15274" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15275" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15276" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15277" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15278" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15279" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15280" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-15281" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15282" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15283" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15284" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15285" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15286"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15287" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15288" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15289" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15290" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15291" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15292" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15293" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15294"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15295" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15296" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15297" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15298" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-15299"><span class="mrow" id="MathJax-Span-15300"><span class="mspace" id="MathJax-Span-15301" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15302" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-15303" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15304" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15305" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-15306" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15307" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15308" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15309" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-15310" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15311" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15312" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-15313" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15314" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-15315" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-15316" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15317" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15318" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15319" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15320" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15321" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15322" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15323" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15324" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15325" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15326" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15327" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15328" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15329" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-15330" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15331" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-15332" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15333" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15334" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15335" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15336" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15337" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-15338" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15339" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15340" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15341" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15342" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15343" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-15344" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15345" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15346" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15347" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15348" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15349" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15350" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15351" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15352" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15353" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15354" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15355" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15356" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15357"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15358" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15359" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15360" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15361" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15362" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15363" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15364" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15365" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15366" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15367" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15368" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15369" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15370" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15371" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15372" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15373" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15374" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15375" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15376" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15377"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15378" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15379" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15380" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15381" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15382" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15383" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15384" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15385" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-15386" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15387" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15388" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15389" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15390" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15391" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15392" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15393" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15394" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15395" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15396" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15397" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15398" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15399"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15400" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15401" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15402" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15403" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15404" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-15405" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15406" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15407" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15408" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15409" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15410" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15411" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15412" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15413" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15414" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15415" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15416" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15417" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15418" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15419"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15420" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15421" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15422" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(35.3px 19360px 56px -9px); top: 0.3px; left: 0px;"><span class="mtd" id="MathJax-Span-15423"><span class="mrow" id="MathJax-Span-15424"><span class="mspace" id="MathJax-Span-15425" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15426" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15427" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-15428" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15429"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15430" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15431" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15432" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≺</span><span class="mi" id="MathJax-Span-15433" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-15434" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-15435"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15436" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15437" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 86px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.8px; vertical-align: -54.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-587">\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)
@@ -2918,28 +2574,14 @@
 \quad\Rightarrow
 gen_1 \prec gen_2
 \end{array}</script></div>
-<div class="constraint" number="43" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="43" id="wasStartedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasStartedBy-ordering">Constraint 43 (wasStartedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-588-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15438"><span style="display: inline-block; position: relative; width: 644px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15439"><span class="mtable" id="MathJax-Span-15440" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 638px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 638px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15441"><span class="mrow" id="MathJax-Span-15442"><span class="mi" id="MathJax-Span-15443" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15444" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15445" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15446" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15447" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15448" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-15449" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15450" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15451" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15452" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-15453" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15454" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15455" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15456" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15457" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15458" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15459" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15460" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15461" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15462" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15463" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15464" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15465" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15466" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15467" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15468" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15469" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15470" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15471" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15472" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15473" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15474" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15475" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15476" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15477" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15478"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15479" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15480" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15483" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15485" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15486"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15487" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15488" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15489" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15490" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-15491"><span class="mrow" id="MathJax-Span-15492"><span class="mspace" id="MathJax-Span-15493" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15494" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-15495" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15496" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15497" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-15498" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15499" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15501" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15502" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15503" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15504" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15505" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15506" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15507" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15508" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15509" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15510" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15511" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15512" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15513" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15514" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15515" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15516" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15517" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15518" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15519" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15520" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15521" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15522" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15523" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15524" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15525" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15526" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15527"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15528" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15529" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15530" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15531" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15532" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15533" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15534" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15535" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-15536" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15537" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15538" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15539" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15540" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15541" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15542" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15543" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15544" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15545" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15546" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15547" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15548" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15549" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-15550" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15551" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15552" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15553" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15554" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15555" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15556" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15557" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15558" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15559" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15560" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15561" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15562" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15563" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15564" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15565" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15566" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15567"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15568" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15569" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15570" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-15571"><span class="mrow" id="MathJax-Span-15572"><span class="mspace" id="MathJax-Span-15573" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15574" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15575" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-15576" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15577" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15578" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-15579" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-15580" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15581" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15582" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15583" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-588">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-588-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-588">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-589-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-589">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-589-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15584"><span style="display: inline-block; position: relative; width: 647px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15585"><span class="mtable" id="MathJax-Span-15586" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 641px; height: 0px;"><span style="position: absolute; clip: rect(68.2px 19360px 139.2px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 641px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15587"><span class="mrow" id="MathJax-Span-15588"><span class="mi" id="MathJax-Span-15589" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15590" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15591" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15601" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15602" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15603" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15604" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15605" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15606" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15607" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15608" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15609" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15610" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15611" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15612" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15613" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15614" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15615" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15616" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15617" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15618" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15619" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15620" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15621" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15622" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15623" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15624"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15625" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15626" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15627" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15628" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15629" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15630" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15631" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15632"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15633" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15634" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15635" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15636" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-15637"><span class="mrow" id="MathJax-Span-15638"><span class="mspace" id="MathJax-Span-15639" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15640" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-15641" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15642" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15643" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-15644" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15645" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15646" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15647" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15648" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15649" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15650" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15651" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15652" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15653" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15654" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15655" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15656" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15657" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-15658" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15659" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15660" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15661" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15662" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15663" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15664" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15665" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15666" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15667" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15668" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15669" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15670" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15671" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15672" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15673" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15674" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15675"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15676" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15677" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15678" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15679" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15680" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15681" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15682" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15683" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-15684" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15685" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-15686" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15687" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15688" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15689" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15690" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15691" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15692" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15693" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15694" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15695" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15696" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15697" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15698" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15699" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-15700" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15701" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15702" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15703" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15704" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15705" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15706" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15707" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15709" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15710" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15711" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15712" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15713" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15714" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15715"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15716" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15717" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15718" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 54px -9px); top: 1.2px; left: 0px;"><span class="mtd" id="MathJax-Span-15719"><span class="mrow" id="MathJax-Span-15720"><span class="mspace" id="MathJax-Span-15721" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15722" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15723" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-15724" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15725" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15726" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15727" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-15728" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-15729" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-15730" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15731" style="font-family: STIXGeneral-Italic;">v</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.6px; vertical-align: -55.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-589">\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)
@@ -2947,28 +2589,14 @@
 \quad\Rightarrow
 start \preceq inv
 \end{array}</script></li></ol></div>
-<div class="constraint" number="44" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="44" id="wasEndedBy-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasEndedBy-ordering">Constraint 44 (wasEndedBy-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-590-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15732"><span style="display: inline-block; position: relative; width: 632px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15733"><span class="mtable" id="MathJax-Span-15734" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 626px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 626px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15735"><span class="mrow" id="MathJax-Span-15736"><span class="mi" id="MathJax-Span-15737" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15738" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15739" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15740" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15741" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15742" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-15743" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15744" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15745" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15746" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15747" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15748" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15749" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15750" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15751" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15752" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15753" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15754" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15755" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15756" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15757" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15758" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15759" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15760" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15761" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15762" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15763" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15764" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15765" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15766" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15767" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15768" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15769" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15770"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15771" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15772" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15773" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15774" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15775" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15776" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15777" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15778"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15779" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15780" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15781" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15782" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-15783"><span class="mrow" id="MathJax-Span-15784"><span class="mspace" id="MathJax-Span-15785" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15786" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-15787" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15788" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15789" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-15790" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15791" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15792" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15793" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15794" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15795" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15796" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15797" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15798" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15799" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15800" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15801" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-15802" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15803" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15804" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15805" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15806" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15807" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15808" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15809" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15810" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15811" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15812" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15813" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15814" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15815" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15816" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15817" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15818" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15819"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15820" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15821" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15822" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15823" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15824" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15825" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15826" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15827" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15828" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15829" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15830" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15831" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15832" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15833" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15834" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15835" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15836" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15837" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15838" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15839" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15840" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15841" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15842" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15843" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15844" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15845" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15846" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15847" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15848" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15849" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15850" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15851" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15852" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15853" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15854" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15855"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15856" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15857" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15858" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-15859"><span class="mrow" id="MathJax-Span-15860"><span class="mspace" id="MathJax-Span-15861" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-15862" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-15863" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-15864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15865" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-15866" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-15867" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-15868" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15869" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-590">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-590-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-590">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-591-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-591">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-591-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-15870"><span style="display: inline-block; position: relative; width: 635px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-15871"><span class="mtable" id="MathJax-Span-15872" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 629px; height: 0px;"><span style="position: absolute; clip: rect(68.8px 19360px 140.8px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 629px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-15873"><span class="mrow" id="MathJax-Span-15874"><span class="mi" id="MathJax-Span-15875" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-15876" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15877" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15878" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15879" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15880" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-15881" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15882" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-15883" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15884" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15885" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15886" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15887" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15888" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15889" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15890" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15891" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15892" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15893" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15894" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15895" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15896" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15897" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15898" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15899" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15900" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15901" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15902" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15903" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15904" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15905" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15907" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15908"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15909" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15910" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15913" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15914" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15915" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15916"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15917" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15918" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15919" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-15920" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-15921"><span class="mrow" id="MathJax-Span-15922"><span class="mspace" id="MathJax-Span-15923" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-15924" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-15925" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15926" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15927" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-15928" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15929" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15930" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15931" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15932" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15933" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15934" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15935" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15936" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15937" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-15938" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15939" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-15940" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15941" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15942" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15943" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15944" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15945" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15946" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15947" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15948" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15949" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15950" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15951" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15953" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15954" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15955"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15956" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15957" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15958" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-15959" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-15960" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-15961" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15962" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-15963" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-15964" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15965" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-15966" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15967" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-15968" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15969" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15970" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-15971" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15972" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-15973" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-15974" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-15975" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-15976" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-15977" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-15978" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-15979" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-15980" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15981" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-15982" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15983" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15984" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-15985" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15986" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-15987" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15988" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-15989" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-15991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-15992" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15993" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-15994" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-15995"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-15996" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-15997" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-15998" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54px -9px); top: 1.8px; left: 0px;"><span class="mtd" id="MathJax-Span-15999"><span class="mrow" id="MathJax-Span-16000"><span class="mspace" id="MathJax-Span-16001" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-16002" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-16003" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-16004" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16005" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-16006" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-16007" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-16008" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16009" style="font-family: STIXGeneral-Italic;">v</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.1px; vertical-align: -55.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-591">\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)
@@ -2976,14 +2604,7 @@
 \quad\Rightarrow
 end \preceq inv
 \end{array}</script></li></ol></div>
-<div class="constraint" number="45" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-592-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-592">\begin{array}[t]{l}
+<div class="constraint" number="45" id="specialization-generation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-generation-ordering">Constraint 45 (specialization-generation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-592-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16010"><span style="display: inline-block; position: relative; width: 877px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-16011"><span class="mtable" id="MathJax-Span-16012" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 871px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 871px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-16013"><span class="mrow" id="MathJax-Span-16014"><span class="mi" id="MathJax-Span-16015" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-16016" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-16017" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16018"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16019" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16020" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16021" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16022" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-16023" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16024"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16025" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16026" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16027" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16028" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16029" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16030" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16031" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16032" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16033" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16034" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16035" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16036" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16037" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16038" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16039" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16040" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16041" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16042" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16043" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16044" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16045" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16046" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16047" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16048" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16049" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16050" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16051" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16052" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16053" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16054" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16055" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16056"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16057" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16058" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16059" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16060" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16061" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16062" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16063" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16064"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16065" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16066" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16067" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-16068" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-16069"><span class="mrow" id="MathJax-Span-16070"><span class="mspace" id="MathJax-Span-16071" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-16072" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16073" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-16074" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16075" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-16076" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16077" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16078" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-16079" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16080" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-16081" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16082" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16083" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16084" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16085" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16086" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-16087" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-16088" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-16089"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16090" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16091" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16092" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16093" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16094" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16095" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16096" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16097" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16098" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16099" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16100" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16101" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-16102" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16103" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16104" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16105" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16106" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16107" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16108" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16109" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16110" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16111" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16112" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16113" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-16114" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16115"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16116" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16117" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16118" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16119" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16120" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16121" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16122" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16123" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16124" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16125" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16126" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16127" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16128" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16129" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16130" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16131" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16132" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16133" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16134" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16135"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16136" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16137" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16138" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16139" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16140" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16141" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16142" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16143" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-16144" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16145" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16146" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16147" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16148" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16149" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16150" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16151" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16152" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16153" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16154" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16155" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-16156" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16157"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16158" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16159" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16160" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16161" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16162" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16163" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16164" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16165" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16166" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16167" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16168" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16169" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16171" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16172" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16173" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16174" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16175" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16176" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16177"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16178" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16179" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16180" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-16181"><span class="mrow" id="MathJax-Span-16182"><span class="mspace" id="MathJax-Span-16183" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-16184" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-16185" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-16186" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16187"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16188" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16189" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16190" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-16191" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-16192" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16193"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16194" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16195" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-592">\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)
@@ -2991,14 +2612,7 @@
 \quad\Rightarrow
 gen_1 \preceq gen_2
 \end{array}</script></div>
-<div class="constraint" number="46" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-593-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-593">\begin{array}[t]{l}
+<div class="constraint" number="46" id="specialization-invalidation-ordering"><div class="ruleTitle"><a class="internalDFN" href="#specialization-invalidation-ordering">Constraint 46 (specialization-invalidation-ordering)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-593-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16196"><span style="display: inline-block; position: relative; width: 883px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-16197"><span class="mtable" id="MathJax-Span-16198" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 877px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.1px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 877px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-16199"><span class="mrow" id="MathJax-Span-16200"><span class="mi" id="MathJax-Span-16201" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-16202" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16203" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16204"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16205" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16206" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16207" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16208" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-16209" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16210"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16211" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16212" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16213" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16214" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16215" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16216" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16217" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16218" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16219" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16220" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16221" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16222" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16223" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16224" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16225" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16226" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16227" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16228" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16229" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16230" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16231" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16232" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16233" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16234" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16235" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16236" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16237" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16238" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16239" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16240" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16241" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16242"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16243" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16244" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16245" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16246" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16247" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16248" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16249" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16250"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16251" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16252" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16253" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-16254" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-16255"><span class="mrow" id="MathJax-Span-16256"><span class="mspace" id="MathJax-Span-16257" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-16258" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16259" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-16260" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16261" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-16262" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16263" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16264" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-16265" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16266" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-16267" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16268" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16269" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16270" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16271" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16272" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-16273" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-16274" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-16275"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16276" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16277" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16278" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16279" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16280" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16281" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16282" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16283" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16284" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16285" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16286" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16287" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-16288" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16289" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-16290" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16291" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-16292" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16293" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16294" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16296" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16297" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16298" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16299" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16300" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16301" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16302" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16303"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16304" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16305" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16306" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16307" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16308" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16309" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16310" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16311" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16312" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16313" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16314" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16315" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16316" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16317" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16318" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16319" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16320" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16321" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16322" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16323"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16324" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16325" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16326" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16327" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16328" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16329" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16330" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16331" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-16332" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16333" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-16334" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16335" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-16336" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16337" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16338" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16339" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16340" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16341" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16342" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16343" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16344" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16345" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16346" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16347"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16348" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16349" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16350" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16351" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16352" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16353" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16354" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16355" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16356" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16357" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16358" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16359" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16360" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16361" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16362" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16363" style="font-family: STIXGeneral-Italic; 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 \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)
@@ -3006,56 +2620,28 @@
 \quad\Rightarrow
 inv_1 \preceq inv_2
 \end{array}</script></div>
-<div class="constraint" number="47" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview">pl</span><span class="MathJax MathJax_Processing" id="MathJax-Element-594-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-594">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="47" id="wasAssociatedWith-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAssociatedWith-ordering">Constraint 47 (wasAssociatedWith-ordering)</a></div><p>In the following inferences, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-594-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16386"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-16387"><span class="mi" id="MathJax-Span-16388" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-16389" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-594">pl</script> may be a placeholder -.</p><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-595-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16390"><span style="display: inline-block; position: relative; width: 1020px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-16391"><span class="mtable" id="MathJax-Span-16392" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 1014px; height: 0px;"><span style="position: absolute; clip: rect(70.2px 19360px 143.2px -9px); top: -86px; left: 0px;"><span style="display: inline-block; position: relative; width: 1014px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-16393"><span class="mrow" id="MathJax-Span-16394"><span class="mi" id="MathJax-Span-16395" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-16396" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16397" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16398" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16399" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16400" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16401" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16402" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-16403" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16404" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16405" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16406"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16407" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16408" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16409" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16410" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-16411" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16412"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16413" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16414" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16415" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16416" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16417" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16418" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16419" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16420" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16421" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16422" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16423" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16424" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16425" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16426" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16427" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16428" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16429" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16430" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16431" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16432" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16433" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16434" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16435" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16436" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16437" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16438" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16439" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16441" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16442" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16443" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16444" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16445" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16446" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16447"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16448" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16449" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16450" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16451" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16452" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16453" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16454" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16455"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16456" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16457" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16458" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-16459" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-16460"><span class="mrow" id="MathJax-Span-16461"><span class="mspace" id="MathJax-Span-16462" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-16463" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-16464" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16465" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16466" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-16467" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16468" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16469" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16470" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-16471" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16472" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16473" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16474" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16475" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16476" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-16477" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16478" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16479" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-16480" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16481" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16482" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16483" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16484" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16485" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16486" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16487" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16488" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16489" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16490" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16491" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16492" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-16493" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-16494" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16495" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16496" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16497" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16498" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16499" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-16500" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16501" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16502" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16503" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16504" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16505" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-16506" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16507" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16508" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16509" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16510" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16511" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16512" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16513" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16514" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16515" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16516" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16517" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16518" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16519"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16520" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16521" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16522" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16523" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16524" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16525" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16526" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16527" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16528" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16529" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16530" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16531" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16532" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16533" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16534" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16535" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16536" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16537" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16538" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16539" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16540" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16541"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16542" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16543" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16544" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16545" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16546" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16547" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16548" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16549" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-16550" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16551" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-16552" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16553" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-16554" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16555" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16556" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16557" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16558" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16559" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16560" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16561" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16562" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16563" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16564" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16565"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16566" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16567" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16568" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16569" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16570" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16571" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16572" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16573" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16574" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16575" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16576" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16577" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16578" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16579" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16580" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16581" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16582" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16583" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16584"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16585" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16586" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16587" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 54.9px -9px); top: 2.3px; left: 0px;"><span class="mtd" id="MathJax-Span-16588"><span class="mrow" id="MathJax-Span-16589"><span class="mspace" id="MathJax-Span-16590" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-16591" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-16592" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-16593" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16594" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16595" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16596"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16597" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16598" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16599" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-16600" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-16601" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16602"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16603" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16604" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 86px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.6px; vertical-align: -56.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-595">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-595-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-595">\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">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-596-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16605"><span style="display: inline-block; position: relative; width: 1005px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-16606"><span class="mtable" id="MathJax-Span-16607" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 999px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 999px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-16608"><span class="mrow" id="MathJax-Span-16609"><span class="mi" id="MathJax-Span-16610" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-16611" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16612" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16613" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16614" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16615" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16616" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16617" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-16618" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16619"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16620" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16621" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16622" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16623" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-16624" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16625"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16626" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-16627" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16628" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16629" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16630" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16631" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16632" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16633" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16634" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16635" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16636" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16637" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16638" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16639" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16640" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16641" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16642" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16643" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16644" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16645" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16646" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16647" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16648" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16649" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16650" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16651" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16652" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16653" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16654" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16655" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16656" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16657" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16658" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16659" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16660"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16661" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16662" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16663" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16664" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16665" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16666" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16667" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16668"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16669" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16670" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16671" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-16672" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-16673"><span class="mrow" id="MathJax-Span-16674"><span class="mspace" id="MathJax-Span-16675" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-16676" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-16677" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16678" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16679" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-16680" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16681" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16682" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16683" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-16684" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16685" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16686" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16687" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16688" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16689" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-16690" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16691" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16692" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-16693" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16694" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16695" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16696" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16697" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16698" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16699" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16700" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16701" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16702" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16703" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16704" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16705" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-16706" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-16707" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16708" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16709" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16710" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16711" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16712" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-16713" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16714" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16715" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16716" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16717" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16718" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-16719" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16720" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16721" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16722" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16723" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16724" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16725" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16726" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16727" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16728" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16729" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16730" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-16731" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16732"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16733" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16734" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16735" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16736" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16737" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16738" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16739" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16740" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16741" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16742" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16743" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16744" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16745" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16748" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16749" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16750" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16751"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16752" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16753" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16754" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16755" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16756" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16757" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16758" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16759" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16760" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16761" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16762" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16763" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16764" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16765" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16766" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16767" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16768" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16769"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16770" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-16771" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16772" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16773" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16774" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16775" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16776" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16777" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16778" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16779" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16780" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16781" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16782" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16783" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16784" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16785" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16786" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16787" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16788" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16789" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16790" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16791"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16792" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16793" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16794" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 56px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-16795"><span class="mrow" id="MathJax-Span-16796"><span class="mspace" id="MathJax-Span-16797" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-16798" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-16799" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-16800" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-16801"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16802" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16803" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16804" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-16805" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-16806" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16807"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16808" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-16809" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 88px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-596">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-596-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-596">\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">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-597-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-16810"><span style="display: inline-block; position: relative; width: 1012px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-16811"><span class="mtable" id="MathJax-Span-16812" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 1006px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 1006px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-16813"><span class="mrow" id="MathJax-Span-16814"><span class="mi" id="MathJax-Span-16815" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-16816" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16817" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16818" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16819" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16820" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16821" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16822" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-16823" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16824" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16825" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16826"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16827" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16828" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16829" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16830" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-16831" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16832"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16833" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-16834" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16835" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16836" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16837" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16838" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16839" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16840" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16841" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16842" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16843" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16844" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16845" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16846" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16847" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16848" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16849" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16850" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16851" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16852" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16853" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16854" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16855" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16856" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16857" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16858" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16859" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16860" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16861" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16862" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16863" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16864" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16865" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16866" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16867"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16868" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16869" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16870" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16871" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16872" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16873" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16874" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16875"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16876" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16877" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16878" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-16879" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-16880"><span class="mrow" id="MathJax-Span-16881"><span class="mspace" id="MathJax-Span-16882" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-16883" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-16884" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16885" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16886" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-16887" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16888" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16889" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16890" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-16891" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16892" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16893" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16895" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16896" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-16897" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-16898" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16899" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-16900" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16901" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16902" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16903" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16904" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-16905" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-16906" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16907" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16908" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16909" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16910" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-16913" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-16914" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16915" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16916" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16917" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16918" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16919" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-16920" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16921" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16922" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16923" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16924" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16925" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-16926" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16927" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16928" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16929" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16930" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16931" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16932" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16933" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16934" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16935" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16936" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16937" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16938" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16939"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16940" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16941" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16942" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16943" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-16944" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16945" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16946" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16947" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16948" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16949" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16950" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16951" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16952" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16953" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16954" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16955" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16956" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16957" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16958" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16959" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-16960" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-16961"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16962" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-16963" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16964" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-16965" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-16966" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-16967" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-16968" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-16969" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-16970" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-16971" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16972" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16973" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-16974" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-16975" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-16976" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-16977" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-16978" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-16979"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16980" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-16981" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16982" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16983" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16984" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-16985" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16986" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16987" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-16988" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16989" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16990" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16991" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-16992" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16993" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-16994" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-16995" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-16996" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-16997" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-16998" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-16999" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17000" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17001" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17002"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17003" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17004" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17005" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54.9px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-17006"><span class="mrow" id="MathJax-Span-17007"><span class="mspace" id="MathJax-Span-17008" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-17009" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-17010" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-17011" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17012" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17013" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17014"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17015" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17016" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17017" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-17018" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-17019" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17020"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17021" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-17022" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.2px; vertical-align: -56.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-597">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-597-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-597">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-598-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-598">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-598-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-17023"><span style="display: inline-block; position: relative; width: 1012px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-17024"><span class="mtable" id="MathJax-Span-17025" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 1006px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.8px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 1006px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-17026"><span class="mrow" id="MathJax-Span-17027"><span class="mi" id="MathJax-Span-17028" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-17029" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17030" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17032" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-17033" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-17034" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17035" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-17036" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17037" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17038" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17039"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17040" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17041" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17042" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17043" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-17044" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17045"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17046" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-17047" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17048" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17049" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17050" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17051" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17052" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17053" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17054" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17055" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17056" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17057" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17058" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17059" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17060" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17061" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17062" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17063" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17064" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17065" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17066" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17067" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17068" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17069" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17070" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17071" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17072" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17073" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17074" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17075" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17076" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17077" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17078" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17079" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17080"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17081" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17082" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17083" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17084" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17085" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17086" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17087" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17088"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17089" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17090" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17091" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-17092" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-17093"><span class="mrow" id="MathJax-Span-17094"><span class="mspace" id="MathJax-Span-17095" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-17096" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-17097" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17098" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17099" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-17100" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17101" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17102" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-17103" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-17104" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17105" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17107" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17108" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17109" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-17110" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17111" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17112" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-17113" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17114" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17115" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17116" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17117" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-17118" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-17119" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17120" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17121" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17122" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17123" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17124" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17125" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-17126" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-17127" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17128" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17129" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17130" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17131" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17132" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17133" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17134" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17135" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17136" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17137" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17138" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-17139" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17140" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17141" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17142" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17143" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17144" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17145" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17146" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17147" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17148" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17149" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17150" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17151" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17152"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17153" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17154" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17155" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17156" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17157" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17158" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17159" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17160" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17161" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17162" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17163" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17164" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17165" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17166" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17167" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17168" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17169" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17170" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17171" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17172" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17173" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17174" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17175"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17176" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17177" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17178" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17179" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17180" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17181" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17182" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17183" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17184" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17185" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17186" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17187" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17188" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17189" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17190" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17191" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17192" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17193"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17194" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-17195" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17196" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17197" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17198" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17199" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17200" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17201" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17202" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17203" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17204" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17205" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17206" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17207" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17208" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17209" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17210" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17211" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17212" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17214" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17215"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17216" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17217" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17218" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54.9px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-17219"><span class="mrow" id="MathJax-Span-17220"><span class="mspace" id="MathJax-Span-17221" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-17222" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-17223" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-17224" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17226" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17227"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17228" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17229" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17230" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-17231" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-17232" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17233"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17234" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-17235" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.2px; vertical-align: -56.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-598">\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)
@@ -3063,28 +2649,14 @@
 \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 class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="48" id="wasAttributedTo-ordering"><div class="ruleTitle"><a class="internalDFN" href="#wasAttributedTo-ordering">Constraint 48 (wasAttributedTo-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-599-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-17236"><span style="display: inline-block; position: relative; width: 942px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-17237"><span class="mtable" id="MathJax-Span-17238" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 936px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 936px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-17239"><span class="mrow" id="MathJax-Span-17240"><span class="mi" id="MathJax-Span-17241" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-17242" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17243" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17244" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-17245" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17246" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-17247" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17248"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17249" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17250" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17251" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17252" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-17253" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17254"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17255" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17256" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17257" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17258" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17259" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17260" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17261" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17262" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17263" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17264" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17265" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17266" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17267" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17268" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17269" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17270" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17271" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17272" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17273" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17274" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17275" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17276" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17277" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17278" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17279" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17280" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17281" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17282" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17283" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17284" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17285" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17286" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17287" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17288" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17289"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17290" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17291" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17292" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17293" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17294" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17295" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17296" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17297"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17298" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17299" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17300" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-17301" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-17302"><span class="mrow" id="MathJax-Span-17303"><span class="mspace" id="MathJax-Span-17304" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-17305" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-17306" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17307" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17308" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-17309" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17310" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17311" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17312" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17313" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-17314" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-17315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17316" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17317" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17318" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-17319" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-17320" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17321" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17322" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17323" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-17324" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17325" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17326" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17327" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17328" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17329" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17330" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17331" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17332" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17333" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17334" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17335" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17336" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17337" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17338" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17339" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17340" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-17341" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17342" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17343" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17344" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17345" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17346" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17347" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17348" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17349" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17350" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17351" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17352" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-17353" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17354"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17355" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17356" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17357" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17358" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17359" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17360" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17361" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17362" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17363" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17364" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17365" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17366" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17367" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17368" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17369" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17370" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17371" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17372" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17373"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17374" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17375" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17376" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17377" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17378" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17379" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17380" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17381" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-17382" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17383" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17384" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17385" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17386" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17387" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17388" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17389" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17390" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17391" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17392" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17393" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-17394" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17395"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17396" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17397" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17398" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17399" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17400" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17401" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17402" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17403" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17404" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17405" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17406" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17407" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17408" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17409" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17410" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17411" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17412" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17413"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17414" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17415" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17416" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-17417"><span class="mrow" id="MathJax-Span-17418"><span class="mspace" id="MathJax-Span-17419" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-17420" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-17421" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-17422" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17423"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17424" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17425" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17426" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-17427" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-17428" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17429"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17430" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17431" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-599">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-599-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-599">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-600-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-600">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-600-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-17432"><span style="display: inline-block; position: relative; width: 950px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-17433"><span class="mtable" id="MathJax-Span-17434" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 944px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 944px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-17435"><span class="mrow" id="MathJax-Span-17436"><span class="mi" id="MathJax-Span-17437" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-17438" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17439" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17440" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-17441" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17442" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-17443" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17444" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17445" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17446"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17447" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17448" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17449" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17450" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-17451" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17452"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17453" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17454" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17455" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17456" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17457" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17458" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17459" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17460" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17461" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17462" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17463" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17464" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17465" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17466" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17467" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17468" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17469" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17470" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17471" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17472" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17473" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17474" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17475" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17476" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17477" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17478" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17479" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17480" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17481" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17482" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17483" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17484" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17485" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17486" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17487" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17488" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17489" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17490" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17491"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17492" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17493" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17494" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17495" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17496" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17497" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17498" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17499"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17500" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17501" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17502" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-17503" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-17504"><span class="mrow" id="MathJax-Span-17505"><span class="mspace" id="MathJax-Span-17506" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-17507" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-17508" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17509" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17510" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-17511" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17512" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17513" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17514" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17515" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-17516" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-17517" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17518" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17519" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17520" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-17521" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-17522" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17523" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17524" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17525" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-17526" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17527" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17528" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17529" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17530" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17531" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17532" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17533" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17534" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17535" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17536" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17537" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17538" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17539" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17540" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17541" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17542" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-17543" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17544" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17545" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17546" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17547" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17548" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17549" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17550" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17551" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17552" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17553" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17554" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17555" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17556"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17557" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17558" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17559" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17560" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17561" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-17562" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17563" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17564" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17565" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17566" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17567" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17568" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17569" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17570" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17571" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17572" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17573" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17574" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17575" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17576" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17577" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17578" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17579"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17580" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17581" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17582" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17583" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17584" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17585" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17586" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17587" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-17588" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17589" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17590" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17591" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17592" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17593" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17594" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17595" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17596" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17597" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17598" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17599" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-17600" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17601"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17602" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17603" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17604" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17605" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-17606" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17607" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17608" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17609" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17610" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17611" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17612" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17613" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17614" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17615" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17616" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17617" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17618" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17619"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17620" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17621" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17622" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(34.2px 19360px 56px -9px); top: 1.4px; left: 0px;"><span class="mtd" id="MathJax-Span-17623"><span class="mrow" id="MathJax-Span-17624"><span class="mspace" id="MathJax-Span-17625" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-17626" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-17627" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-17628" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17629" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17630" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17631"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17632" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17633" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17634" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-17635" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-17636" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17637"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17638" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17639" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.9px; vertical-align: -55.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-600">\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)
@@ -3092,28 +2664,14 @@
 \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 class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="49" id="actedOnBehalfOf-ordering"><div class="ruleTitle"><a class="internalDFN" href="#actedOnBehalfOf-ordering">Constraint 49 (actedOnBehalfOf-ordering)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-601-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-17640"><span style="display: inline-block; position: relative; width: 1034px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 100.6px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-17641"><span class="mtable" id="MathJax-Span-17642" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 1028px; height: 0px;"><span style="position: absolute; clip: rect(72.8px 19360px 148.6px -9px); top: -89px; left: 0px;"><span style="display: inline-block; position: relative; width: 1028px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-17643"><span class="mrow" id="MathJax-Span-17644"><span class="mi" id="MathJax-Span-17645" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-17646" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17647" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17648" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-17649" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17650" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mi" id="MathJax-Span-17651" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17652"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17653" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17654" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17655" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17656" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">i</span><span class="mi" id="MathJax-Span-17657" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17658"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17659" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17660" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17661" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17662" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17663"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17664" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17665" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17666" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17667" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17668"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17669" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17670" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17671" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17672" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17673" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17674" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17675" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17676" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17677" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17678" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17679" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17680" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17681" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17682" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17683" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17684" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17685" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17686" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17687" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17688" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17689" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17690" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17691" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17692" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17693" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17694" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17695" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17696" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17697" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17698" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17699" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17700"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17701" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17702" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17703" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17704" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17705" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17706" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17707" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17708"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17709" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17710" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17711" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-17712" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -21.4px; left: 0px;"><span class="mtd" id="MathJax-Span-17713"><span class="mrow" id="MathJax-Span-17714"><span class="mspace" id="MathJax-Span-17715" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-17716" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17717" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-17718" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17719" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17720" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17721" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-17722" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17723" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17724" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17725" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-17726" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17727" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-17728" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-17729" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-17730" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-17731" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17732" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17733" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17734" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-17735" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17736" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17737"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17738" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17739" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17740" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17741" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17742"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17743" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17744" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17745" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17746" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17747" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17748" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17749" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17750" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17751" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17752" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17753" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17754" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17755" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17756" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17757" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17758" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-17759" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17760" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17761" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17762" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17763" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17764" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17765" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17766" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17767" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17768" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17769" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17770" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-17771" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17772"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17773" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17774" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17775" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17776" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17777"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17778" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17779" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17780" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17781" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17782" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17783" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17784" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17785" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17786" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17787" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17788" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17789" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17790" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17791" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17792" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17793"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17794" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17795" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17796" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17797" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17798" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17799" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17800" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17801" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-17802" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17803" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-17804" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17805" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-17806" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17807" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17808" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17809" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17810" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17811" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17812" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17813" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17814" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17815" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-17816" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17817"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17818" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17819" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17820" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17821" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17822"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17823" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17824" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17825" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17826" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17827" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17828" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17829" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17830" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17832" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17833" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17834" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17835" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17836" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17837" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17838"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17839" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17840" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17841" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(33.3px 19360px 56px -9px); top: 3.7px; left: 0px;"><span class="mtd" id="MathJax-Span-17842"><span class="mrow" id="MathJax-Span-17843"><span class="mspace" id="MathJax-Span-17844" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-17845" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-17846" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-17847" style="font-family: STIXGeneral-Italic;">e</span><span class="msubsup" id="MathJax-Span-17848"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17849" style="font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17850" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17851" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-17852" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-17853" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17854"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17855" style="font-family: STIXGeneral-Italic;">v</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17856" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 89px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 74.1px; vertical-align: -57.6px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-601">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-601-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-601">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-602-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-602">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-602-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-17857"><span style="display: inline-block; position: relative; width: 1033px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 101.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-17858"><span class="mtable" id="MathJax-Span-17859" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 1027px; height: 0px;"><span style="position: absolute; clip: rect(72.8px 19360px 148.1px -9px); top: -89px; left: 0px;"><span style="display: inline-block; position: relative; width: 1027px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-17860"><span class="mrow" id="MathJax-Span-17861"><span class="mi" id="MathJax-Span-17862" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-17863" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17865" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-17866" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17867" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">s</span><span class="mi" id="MathJax-Span-17868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17869" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17870" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17871"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17872" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17873" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17874" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17875" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-17876" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-17877"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17878" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-17879" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17880" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17881" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17882"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17883" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17884" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17885" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17886" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17887"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17888" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17889" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17890" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17891" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17892" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17893" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17894" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17895" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17896" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17897" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17898" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-17899" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17900" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17901" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17902" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17903" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17904" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17905" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17906" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-17907" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17908" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17909" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17910" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17911" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17912" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-17913" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17914" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-17915" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17916" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17917" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17918" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17919" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17920" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17921" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17922" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17923" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17924" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17925" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17926" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17927"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17928" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17929" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17930" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17931" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17932" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17933" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17934" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17935"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17936" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-17937" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17938" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-17939" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -21.4px; left: 0px;"><span class="mtd" id="MathJax-Span-17940"><span class="mrow" id="MathJax-Span-17941"><span class="mspace" id="MathJax-Span-17942" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-17943" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17944" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-17945" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17946" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17947" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17948" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-17949" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-17950" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17951" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17952" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-17953" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17954" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-17955" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-17956" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-17957" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-17958" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17959" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17960" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17961" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-17962" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17963" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17964"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17965" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17966" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17967" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17968" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-17969"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-17970" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-17971" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-17972" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17973" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-17974" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-17975" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-17976" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17977" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17978" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17979" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-17980" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-17981" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-17982" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-17983" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17984" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17985" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-17986" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17987" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17988" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-17989" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17990" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-17991" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-17992" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-17993" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-17994" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-17995" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-17996" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-17997" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-17998" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-17999"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18000" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18001" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18002" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18003" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-18004"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18005" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-18006" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18007" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18008" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18009" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-18010" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18011" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18012" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18013" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18014" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18015" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18016" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18017" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18018" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18019" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18020" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18021" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18023" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-18024"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18025" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-18026" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18027" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18028" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18029" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-18030" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-18032" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18033" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18034" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-18035" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18036" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-18037" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-18038" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18039" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18040" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18041" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-18042"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18043" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-18044" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18045" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18046" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-18047"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18048" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-18049" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18050" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18051" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18052" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-18053" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18054" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18055" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18056" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18057" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18058" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18059" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18060" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18061" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18062" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18063" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18064" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18065" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18066" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-18067"><span style="display: inline-block; position: relative; width: 15.5px; height: 0px;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18068" style="font-family: STIXGeneral-Italic;">s</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 7px;"><span class="mn" id="MathJax-Span-18069" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18070" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 54.9px -9px); top: 4.2px; left: 0px;"><span class="mtd" id="MathJax-Span-18071"><span class="mrow" id="MathJax-Span-18072"><span class="mspace" id="MathJax-Span-18073" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18074" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18075" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-18076" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18077" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18078" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="msubsup" id="MathJax-Span-18079"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18080" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18081" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18082" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⪯</span><span class="mi" id="MathJax-Span-18083" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-18084" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-18085"><span style="display: inline-block; position: relative; width: 18.9px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18086" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10.5px;"><span class="mn" id="MathJax-Span-18087" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 89px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 74.6px; vertical-align: -58.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-602">\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)
@@ -3127,266 +2685,133 @@
 <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 class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview">\begin{array}[t]{l}
+<div class="constraint" number="50" id="typing"><div class="ruleTitle"><a class="internalDFN" href="#typing">Constraint 50 (typing)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-603-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-18088"><span style="display: inline-block; position: relative; width: 174px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.4px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-18089"><span class="mtable" id="MathJax-Span-18090" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 168px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.4px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 168px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-18091"><span class="mrow" id="MathJax-Span-18092"><span class="mi" id="MathJax-Span-18093" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-18094" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-18095" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18096" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18097" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18098" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18099" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18100" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18101" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-18102" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 55px -9px); top: -23.5px; left: 0px;"><span class="mtd" id="MathJax-Span-18103"><span class="mrow" id="MathJax-Span-18104"><span class="mspace" id="MathJax-Span-18105" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18106" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18107" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18108" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18126" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18127" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18128" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18129" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18130" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18131" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18132" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-18133" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18134" style="font-family: STIXGeneral-Italic; 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top: -22.2px; left: 0px;"><span class="mtd" id="MathJax-Span-18157"><span class="mrow" id="MathJax-Span-18158"><span class="mspace" id="MathJax-Span-18159" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18160" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18161" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-18162" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18163" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18164" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18165" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18166" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18167" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-18168" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18169" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18171" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18172" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18173" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18174" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 2.6px; left: 0px;"><span class="mtd" id="MathJax-Span-18175"><span class="mrow" id="MathJax-Span-18176"><span class="mspace" id="MathJax-Span-18177" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18178" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18179" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18180" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18181" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18182" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18183" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18184" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18185" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18186" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18187" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-18188" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18189" style="font-family: STIXGeneral-Italic; 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position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18204" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18205" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18206" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18207" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18208" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18209" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18210" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18211" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18212" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18214" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18215" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18216" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-18217" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.9px 19360px 55px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-18218"><span class="mrow" id="MathJax-Span-18219"><span class="mspace" id="MathJax-Span-18220" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18221" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18222" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18223" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18224" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18225" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18226" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18227" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18228" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18229" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18230" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-18231" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18232" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18233" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18234" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18235" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18236" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 14.1px; height: 0px;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18237" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 5.7px;"><span class="mn" id="MathJax-Span-18238" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18239" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18240" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18241" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18242" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18243" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18244" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18245" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.5px; left: 0px;"><span class="mtd" id="MathJax-Span-18246"><span class="mrow" id="MathJax-Span-18247"><span class="mspace" id="MathJax-Span-18248" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18249" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18250" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18251" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18252" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18253" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18254" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18255" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18256" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18257" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-18258" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18259" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18260" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18261" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18262" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18263" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18264" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18265" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-606-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-18268"><span style="display: inline-block; position: relative; width: 331px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.9px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-18269"><span class="mtable" id="MathJax-Span-18270" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 325px; height: 0px;"><span style="position: absolute; clip: rect(70.2px 19360px 142.9px -9px); top: -86px; left: 0px;"><span style="display: inline-block; position: relative; width: 325px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-18271"><span class="mrow" id="MathJax-Span-18272"><span class="mi" id="MathJax-Span-18273" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-18274" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-18275" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18276" style="font-family: STIXGeneral-Italic; 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vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18314" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18315" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18316" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18317" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18318" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18319" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18320" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18321" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18322" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-18323" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18324" style="font-family: STIXGeneral-Italic; 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 \\
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 \\
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overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18537" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-18538"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18539" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18540" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18541" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18542" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18543" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18544" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.3px; vertical-align: -56.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-608">\begin{array}[t]{l}
 \forall inf,a_2,a_1,t,attrs.~
 \\
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 \\
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 typeOf(a_1,activity) \wedge typeOf(a_2,activity)
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-\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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-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-609-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-609">\begin{array}[t]{l}
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overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18600" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18601" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18602" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18603" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18604" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18605" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18606" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18607" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18608" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-18609" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18610" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18611" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18612" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18613" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18614" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18615" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18616" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18617" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18618" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18619" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18661" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18662" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18663" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18664" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18665" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18666" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18667" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18668" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18669" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18670" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18671" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18672" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18673" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18674" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18675" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-18676" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18677" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-18678" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18679" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18680" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18681" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18682" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18683" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-609">\begin{array}[t]{l}
 \forall start,a_2,e,a_1,t,attrs.~
 \\
 \qquad wasStartedBy(start,a_2,e,a_1,t,attrs)
 \\
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 typeOf(a_1,activity) \wedge typeOf(a_2,activity) \wedge typeOf(e,entity)
-\end{array}</script></li><li><span class="MathJax_Preview">\begin{array}[t]{l}
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overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-18693" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18694" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18695" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18696" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18697" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18698" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-18699" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18700" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18701" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18702" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18703" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18704" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; 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padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-18713"><span class="mrow" id="MathJax-Span-18714"><span class="mspace" id="MathJax-Span-18715" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18716" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-18717" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18718" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-18719" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18720" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18721" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; 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position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18732" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18733" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18734" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18735" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-18736" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18737" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18738" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18739" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18740" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18741" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18742" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18743" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18744" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18746" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18747" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18748" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.7px; left: 0px;"><span class="mtd" id="MathJax-Span-18749"><span class="mrow" id="MathJax-Span-18750"><span class="mspace" id="MathJax-Span-18751" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18752" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18753" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18754" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18755" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18757" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18758" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18759" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-18760"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18761" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18762" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18763" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18764" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18765" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18766" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18767" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18768" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18769" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18770" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18771" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18772" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18773" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18774" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18775" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18776" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18777" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18778" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18779" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18780" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-18781"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18782" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18783" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18784" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18785" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18786" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18787" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18788" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18789" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18790" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18791" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18792" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18793" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18794" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18795" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18796" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18797" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18798" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18799" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18800" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18801" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18802" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-18803" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18804" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-18805" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18806" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18807" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18808" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18809" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18810" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-610">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-610-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-610">\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-611-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-611">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-611-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-18811"><span style="display: inline-block; position: relative; width: 331px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.5px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-18812"><span class="mtable" id="MathJax-Span-18813" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 325px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.5px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 325px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-18814"><span class="mrow" id="MathJax-Span-18815"><span class="mi" id="MathJax-Span-18816" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-18817" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18818" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18819" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-18820" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18821" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-18822" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18823" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-18824" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18825" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18826" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18827" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18828" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18829" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18830" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18831" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18832" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-18833" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-18834"><span class="mrow" id="MathJax-Span-18835"><span class="mspace" id="MathJax-Span-18836" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18837" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-18838" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18839" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-18840" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-18841" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18842" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18843" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18844" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-18845" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18846" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-18847" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18848" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18849" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18850" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-18851" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-18852" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18853" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18854" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18855" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18856" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-18857" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18858" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-18859" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18860" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-18861" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18862" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-18863" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18864" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18865" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18866" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18867" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18868" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18869" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.5px; left: 0px;"><span class="mtd" id="MathJax-Span-18870"><span class="mrow" id="MathJax-Span-18871"><span class="mspace" id="MathJax-Span-18872" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-18873" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-18874" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18875" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18876" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18877" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18878" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18879" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18880" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18881" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-18882" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18883" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18884" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-18885" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18886" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18887" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18888" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18889" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18890" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18891" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18892" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18893" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18894" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-18895" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-18896" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18897" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-18898" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-18899" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18900" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-18901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-18903" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18904" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18905" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18907" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-18908" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72px; vertical-align: -55.5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-611">\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">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-612-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-18909"><span style="display: inline-block; position: relative; width: 694px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 101.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-18910"><span class="mtable" id="MathJax-Span-18911" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 688px; height: 0px;"><span style="position: absolute; clip: rect(73.8px 19360px 150.1px -9px); top: -90px; left: 0px;"><span style="display: inline-block; position: relative; width: 688px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-18912"><span class="mrow" id="MathJax-Span-18913"><span class="mi" id="MathJax-Span-18914" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-18915" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18916" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-18917" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18918" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18919" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-18920" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18921" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18922" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18923" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-18924" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18925" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18926" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-18927" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18928" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18929" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-18930" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18931" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-18932" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18933" style="font-family: STIXGeneral-Italic;">u</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18934" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18935" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-18936" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-18937" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18939" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18940" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-18941" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-18942" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -21.4px; left: 0px;"><span class="mtd" id="MathJax-Span-18943"><span class="mrow" id="MathJax-Span-18944"><span class="mspace" id="MathJax-Span-18945" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-18946" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-18947" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-18948" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18949" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-18950" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-18951" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-18952" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-18953" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18954" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-18955" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18956" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18957" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-18958" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-18959" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18960" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-18961" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-18962" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-18963" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-18964" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-18965"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18966" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-18967" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18968" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18969" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18970" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-18971" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-18972" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-18973" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-18974" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-18975" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-18976" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-18977" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-18978"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-18979" style="font-family: STIXGeneral-Italic;">u</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-18980" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-18981" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-18982" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-18983" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-18984" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-18985" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-18986" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-18987" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18988" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18989" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18990" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-18991" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-18992" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-18993" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-18994" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-18995" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-18996" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-18997" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-18998" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-18999" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-19000" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19001" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19002" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19003" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19004" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19005" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19006" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19007" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19008" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19009" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-19010" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19011" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19012" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19013" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19014" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19015" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19016" style="font-family: STIXGeneral-Italic;">u</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-19017" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19018" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19019" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19020" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19021" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19022" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19023" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-19024" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 4.1px; left: 0px;"><span class="mtd" id="MathJax-Span-19025"><span class="mrow" id="MathJax-Span-19026"><span class="mspace" id="MathJax-Span-19027" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19028" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19029" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19030" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19031" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19032" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19033" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19034" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19035" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19036"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19037" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19038" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19039" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19040" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-19041" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19042" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19044" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19045" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19046" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19047" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19048" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19049" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19050" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19051" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19052" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19053" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19054" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19055"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19056" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19057" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19058" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19059" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19060" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19061" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19062" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19063" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-19064" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19065" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19066" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19067" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19068" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19069" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19070" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19071" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19072" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19073" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19074" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19075" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19076" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-19077" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19078" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19079" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19080" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19081" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19082" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-19083" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19084" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19085" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19086" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 90px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 74.6px; vertical-align: -58.1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-612">\begin{array}[t]{l}
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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-613-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-19087"><span style="display: inline-block; position: relative; width: 368px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.1px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-19088"><span class="mtable" id="MathJax-Span-19089" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 362px; height: 0px;"><span style="position: absolute; clip: rect(70.8px 19360px 144.1px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 362px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-19090"><span class="mrow" id="MathJax-Span-19091"><span class="mi" id="MathJax-Span-19092" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-19093" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19094" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-19095" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19096" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19097" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19098" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19099" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19100" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19101" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19102" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19103" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19104" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19105" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19106" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19107" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19108" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-19109" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-19110" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-19111"><span class="mrow" id="MathJax-Span-19112"><span class="mspace" id="MathJax-Span-19113" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19114" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-19115" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19116" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-19117" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-19118" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19119" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19120" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19121" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-19122" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19123" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-19124" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-19125" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19126" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-19127" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-19128" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19129" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19130" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-19131" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19132" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19133" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19134" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19135" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19136" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19137" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19138" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19139" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-19140" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-19141" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-19142" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-19143" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-19144" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-19145" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19146" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19147" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19149" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19150" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-19151" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.1px; left: 0px;"><span class="mtd" id="MathJax-Span-19152"><span class="mrow" id="MathJax-Span-19153"><span class="mspace" id="MathJax-Span-19154" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19155" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19156" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19157" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19158" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19159" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19160" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19161" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19162" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19163"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19164" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19165" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19166" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19167" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-19168" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19169" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19170" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19171" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19172" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19173" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19174" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19175" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19176" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19177" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19178" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19179" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19180" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19181" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19182"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19183" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19184" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19185" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19186" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19187" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19188" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19189" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19190" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-19191" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19192" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19193" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19194" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; 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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-614-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-19195"><span style="display: inline-block; position: relative; width: 329px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-19196"><span class="mtable" id="MathJax-Span-19197" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 323px; height: 0px;"><span style="position: absolute; clip: rect(71.8px 19360px 146.8px -9px); top: -88px; left: 0px;"><span style="display: inline-block; position: relative; width: 323px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-19198"><span class="mrow" id="MathJax-Span-19199"><span class="mi" id="MathJax-Span-19200" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-19201" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19202" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; 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 \forall id,e,ag,attrs.~
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 typeOf(e,entity) \wedge typeOf(ag,agent)
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top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-19310"><span class="mrow" id="MathJax-Span-19311"><span class="mspace" id="MathJax-Span-19312" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19313" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19314" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-19315" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19316" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-19317" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-19318" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; 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vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19363" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19364" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19365" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19366" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19367" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19368" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19369" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19370" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19371" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-19372" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19373" style="font-family: STIXGeneral-Italic; 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-\forall id,a,ag,pl,attrs.~
-\\
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padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19480" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19481" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19482" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19483" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19484" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19485" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19486" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-19487" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19488" style="font-family: STIXGeneral-Italic; 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-typeOf(a,activity) \wedge typeOf(ag,agent)
-\end{array}</script></li><li><span class="MathJax_Preview">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-617-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-19514"><span style="display: inline-block; position: relative; width: 517px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 101.8px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-19515"><span class="mtable" id="MathJax-Span-19516" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 511px; height: 0px;"><span style="position: absolute; clip: rect(73.8px 19360px 150.8px -9px); top: -90px; left: 0px;"><span style="display: inline-block; position: relative; width: 511px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-19517"><span class="mrow" id="MathJax-Span-19518"><span class="mi" id="MathJax-Span-19519" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-19520" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19521" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-19522" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19523" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-19524"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19525" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19526" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19527" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19528" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-19529"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19530" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19531" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19532" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19533" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-19534" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19535" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19536" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19537" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19538" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19539" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-19540" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-19541" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -9px); top: -21.4px; left: 0px;"><span class="mtd" id="MathJax-Span-19542"><span class="mrow" id="MathJax-Span-19543"><span class="mspace" id="MathJax-Span-19544" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19545" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19546" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19547" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19548" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19549" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-19550" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19551" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19552" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-19553" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19554" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-19555" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19556" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-19557" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-19558" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19559" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19560" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19561" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19562" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-19563" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19564" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-19565"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19566" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19567" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19568" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19569" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-19570"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19571" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19572" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19573" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19574" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-19575" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19576" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19577" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19578" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19579" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19580" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-19581" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56.7px -9px); top: 4.1px; left: 0px;"><span class="mtd" id="MathJax-Span-19582"><span class="mrow" id="MathJax-Span-19583"><span class="mspace" id="MathJax-Span-19584" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19585" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19586" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19587" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19588" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19589" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19590" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19591" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19592" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19593" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-19594"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19595" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19596" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19597" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19598" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19599" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-19600" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19601" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19602" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-19603" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19604" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19605" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19606" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19607" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19608" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19609" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19610" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19611" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19612" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-19613"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19614" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-19615" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19616" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19617" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19618" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-19619" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19620" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19621" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-19622" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19623" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19624" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19625" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19626" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19627" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19628" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19629" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19630" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-19631" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-19632" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19633" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-19634" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19635" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19636" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19637" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-19638" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19639" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19640" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19641" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 90px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 75.3px; vertical-align: -58.8px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-617">\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)
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-\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">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-618-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-618">\begin{array}[t]{l}
+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-618-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-19642"><span style="display: inline-block; position: relative; width: 333px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-19643"><span class="mtable" id="MathJax-Span-19644" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 327px; height: 0px;"><span style="position: absolute; clip: rect(71.2px 19360px 144.7px -9px); top: -87px; left: 0px;"><span style="display: inline-block; position: relative; width: 327px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.9px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-19645"><span class="mrow" id="MathJax-Span-19646"><span class="mi" id="MathJax-Span-19647" style="font-family: STIXGeneral-Regular;">∀</span><span class="msubsup" id="MathJax-Span-19648"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19649" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19650" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19651" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19652" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19653" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19654" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19655" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-19656" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-19657"><span class="mrow" id="MathJax-Span-19658"><span class="mspace" id="MathJax-Span-19659" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19660" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19661" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-19662" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19663" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19664" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-19665" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19666" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19667" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19668" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19669" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19670" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19671" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19672"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19673" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19674" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19675" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19676" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19677" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19678" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19679" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.7px; left: 0px;"><span class="mtd" id="MathJax-Span-19680"><span class="mrow" id="MathJax-Span-19681"><span class="mspace" id="MathJax-Span-19682" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19683" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19684" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19685" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19686" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19687" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19688" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19689" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19690" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19691"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19692" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19693" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19694" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19695" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-19696" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19697" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19698" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19699" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19700" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19701" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19702" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19703" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19704" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19705" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19706" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19707" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19708" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19709" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19710"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19711" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19712" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19713" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19714" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-19715" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19716" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19717" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19718" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19719" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19720" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 87px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-618">\begin{array}[t]{l}
 \forall e_2,e_1.~
 \\
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 \\
 \quad\Rightarrow
 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
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-\forall e_2,e_1.~
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-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-619-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-619">\begin{array}[t]{l}
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position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19728" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19729" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19730" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19731" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19732" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19733" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19734" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-19735" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.2px; left: 0px;"><span class="mtd" id="MathJax-Span-19736"><span class="mrow" id="MathJax-Span-19737"><span class="mspace" id="MathJax-Span-19738" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19739" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-19740" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19741" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19742" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-19743" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19744" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19745" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-19746" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19747" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-19748" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-19749" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19750" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19751" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-19752" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19753" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19754" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19755" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19756"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19757" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19758" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19759" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-19760" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19761" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19762" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19763" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.9px 19360px 56px -9px); top: 1.7px; left: 0px;"><span class="mtd" id="MathJax-Span-19764"><span class="mrow" id="MathJax-Span-19765"><span class="mspace" id="MathJax-Span-19766" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-19767" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-19768" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19769" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19770" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19771" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19772" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19773" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-19774" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-19775"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-19776" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-19777" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-19778" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-19779" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-19780" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19781" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19782" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19783" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19784" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-19785" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-19786" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-19787" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19788" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-19789" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-19790" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19791" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-19792" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; 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 \forall e_2,e_1.~
 \\
 \qquad specializationOf(e_2,e_1)
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 typeOf(e_2,entity) \wedge typeOf(e_1,entity)
-\end{array}</script></li><li><span class="MathJax_Preview">\begin{array}[t]{l}
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border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.5px; vertical-align: -55px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-620">\begin{array}[t]{l}
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 \\
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 \\
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-\forall c.~
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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-621-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-19879"><span style="display: inline-block; position: relative; width: 690px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-19880"><span class="mtable" id="MathJax-Span-19881" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 684px; height: 0px;"><span style="position: absolute; clip: rect(69.2px 19360px 141.2px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 684px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 51.2px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-19882"><span class="mrow" id="MathJax-Span-19883"><span class="mi" id="MathJax-Span-19884" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-19885" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-19886" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-19887" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -24.8px; left: 0px;"><span class="mtd" id="MathJax-Span-19888"><span class="mrow" id="MathJax-Span-19889"><span class="mspace" id="MathJax-Span-19890" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-19891" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-19892" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-19893" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-19894" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-19895" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20001" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20002" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20003" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20004" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20005" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20006" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20007" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20008" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20009" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-20010" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.7px; vertical-align: -54.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-621">\begin{array}[t]{l}
 \forall c.~
 \\
 \qquad entity(c,[prov:type = prov:emptyCollection]))
@@ -3404,42 +2829,21 @@
 <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 class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-622-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-622">\begin{array}[t]{l}
+<div class="constraint" number="51" id="impossible-unspecified-derivation-generation-use"><div class="ruleTitle"><a class="internalDFN" href="#impossible-unspecified-derivation-generation-use">Constraint 51 (impossible-unspecified-derivation-generation-use)</a></div><ol><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-622-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20011"><span style="display: inline-block; position: relative; width: 465px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20012"><span class="mtable" id="MathJax-Span-20013" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 459px; height: 0px;"><span style="position: absolute; clip: rect(68.8px 19360px 140.7px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 459px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20014"><span class="mrow" id="MathJax-Span-20015"><span class="mi" id="MathJax-Span-20016" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20017" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20018" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20019" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20020" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20021" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20022" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20023" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20024" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20025" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20026" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20027" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20028" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-20029" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20030" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20031" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20032" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20033" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20034" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-20035" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20036" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-20037"><span class="mrow" id="MathJax-Span-20038"><span class="mspace" id="MathJax-Span-20039" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20040" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20041" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20042" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20043" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-20044" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20045" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20046" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-20047" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20048" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-20049" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20050" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20051" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-20052" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20053" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20054" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-20055" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20056" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20057" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20058" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20059" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20060" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20061" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20062" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20063" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20064" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-20065" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20066" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20067" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20068" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20069" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20070" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20071" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20072" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20073" style="padding-left: 3.6px;"><span style="display: inline-block; 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width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.2px; vertical-align: -56.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-622">\begin{array}[t]{l}
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overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20106" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20107" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20108" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20109" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20110" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20111" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20112" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20113" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20114" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20115" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-20116" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20117" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20118" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; 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overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-20134" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20135" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-20136" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20137" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20138" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-20139" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20140" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20141" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-20142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20143" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20144" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20145" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20146" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20147" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20148" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20149" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20150" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20151" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-20152" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20153" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20154" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20155" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20156" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20157" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20158" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20159" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20160" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20161" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20162" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20163" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20164" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-20165" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20166" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-20167" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20168" style="font-family: STIXGeneral-Italic; 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+\end{array}</script></li><li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-624-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20185"><span style="display: inline-block; position: relative; width: 563px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 99.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20186"><span class="mtable" id="MathJax-Span-20187" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 557px; height: 0px;"><span style="position: absolute; clip: rect(68.8px 19360px 140.7px -9px); top: -85px; left: 0px;"><span style="display: inline-block; position: relative; width: 557px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20188"><span class="mrow" id="MathJax-Span-20189"><span class="mi" id="MathJax-Span-20190" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20191" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20192" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20193" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20194" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20195" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20196" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20197" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20198" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20199" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20200" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20201" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20202" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-20203" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20204" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-20205" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20206" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20207" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20208" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20209" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20210" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-20211" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20212" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -22.1px; left: 0px;"><span class="mtd" id="MathJax-Span-20213"><span class="mrow" id="MathJax-Span-20214"><span class="mspace" id="MathJax-Span-20215" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20216" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20217" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20218" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20219" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-20220" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20221" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20222" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-20223" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20224" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-20225" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20226" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20227" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">n</span><span class="mi" id="MathJax-Span-20228" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20229" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20230" style="font-family: STIXGeneral-Italic;">N<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.2px;"></span></span><span class="mi" id="MathJax-Span-20231" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20232" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20233" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-20234" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20235" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-20236" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20237" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20238" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mi" id="MathJax-Span-20239" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20240" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20241" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-20242" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20243" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20244" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20245" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20246" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20247" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20248" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20249" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20250" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20251" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-20252" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20253" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20254" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20255" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20256" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20257" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20258" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">2</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20259" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20260" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20261" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-20262" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20263" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20264" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-20265" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20266" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-20267" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20268" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-20269" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20270" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20271" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20272" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20273" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20274" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-20275" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 2.8px; left: 0px;"><span class="mtd" id="MathJax-Span-20276"><span class="mrow" id="MathJax-Span-20277"><span class="mspace" id="MathJax-Span-20278" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20279" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20280" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20281" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20282" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20283" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20284" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 85px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 73.2px; vertical-align: -56.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-624">\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)
@@ -3449,17 +2853,10 @@
 \end{array}</script></li></ol></div>
 <div class="proof">
   <p>Each part follows from the fact that the semantics of
-  <span class="MathJax_Preview">wasDerivedFrom</span><span class="MathJax MathJax_Processing" id="MathJax-Element-625-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-625">wasDerivedFrom</script> only allows formulas to hold when either all three
-  of <span class="MathJax_Preview">a,g,u</span><span class="MathJax MathJax_Processing" id="MathJax-Element-626-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-626">a,g,u</script> are <span class="MathJax_Preview">-</span><span class="MathJax MathJax_Processing" id="MathJax-Element-627-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-627">-</script> (denoting <span class="MathJax_Preview">\bot</span><span class="MathJax MathJax_Processing" id="MathJax-Element-628-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-628">\bot</script>) or none of them are.</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-625-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20285"><span style="display: inline-block; position: relative; width: 135px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20286"><span class="mi" id="MathJax-Span-20287" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-20288" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20290" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-20291" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20292" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20294" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20295" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20296" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20297" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20298" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20299" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20300" style="font-family: STIXGeneral-Italic;">m</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.6px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-625">wasDerivedFrom</script> only allows formulas to hold when either all three
+  of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-626-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20301"><span style="display: inline-block; position: relative; width: 46px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20302"><span class="mi" id="MathJax-Span-20303" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-20304" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20305" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-20306" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20307" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-626">a,g,u</script> are <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-627-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20308"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20309"><span class="mo" id="MathJax-Span-20310" style="font-family: STIXGeneral-Regular;">−</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-627">-</script> (denoting <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-628-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20311"><span style="display: inline-block; position: relative; width: 14px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20312"><span class="mi" id="MathJax-Span-20313" style="font-family: STIXGeneral-Regular;">⊥</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.8px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-628">\bot</script>) or none of them are.</p>
   </div>
-<div class="constraint" number="52" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall e.~
-\\
-\qquad specializationOf(e,e)
-\\
-\quad\Rightarrow
-False
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-629-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
+<div class="constraint" number="52" id="impossible-specialization-reflexive"><div class="ruleTitle"><a class="internalDFN" href="#impossible-specialization-reflexive">Constraint 52 (impossible-specialization-reflexive)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-629-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20314"><span style="display: inline-block; position: relative; width: 213px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20315"><span class="mtable" id="MathJax-Span-20316" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 207px; height: 0px;"><span style="position: absolute; clip: rect(66.2px 19360px 135px -9px); top: -82px; left: 0px;"><span style="display: inline-block; position: relative; width: 207px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 51.2px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20317"><span class="mrow" id="MathJax-Span-20318"><span class="mi" id="MathJax-Span-20319" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20320" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-20321" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20322" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -24.8px; left: 0px;"><span class="mtd" id="MathJax-Span-20323"><span class="mrow" id="MathJax-Span-20324"><span class="mspace" id="MathJax-Span-20325" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20326" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20327" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20328" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20329" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20330" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20331" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20332" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20333" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20334" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-20335" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20336" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20337" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20338" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20339" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20340" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20341" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20342" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20343" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-20344" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20345" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-20346" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 0.2px; left: 0px;"><span class="mtd" id="MathJax-Span-20347"><span class="mrow" id="MathJax-Span-20348"><span class="mspace" id="MathJax-Span-20349" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20350" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20351" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20352" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20354" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20355" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 82px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.5px; vertical-align: -54px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-629">\begin{array}[t]{l}
 \forall e.~
 \\
 \qquad specializationOf(e,e)
@@ -3469,18 +2866,11 @@
 \end{array}</script></div>
 <div class="proof">
   <p>This follows from the fact that in the semantics of
-  <span class="MathJax_Preview">specializationOf</span><span class="MathJax MathJax_Processing" id="MathJax-Element-630-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-630">specializationOf</script>, the two entities denoted by the first and second
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-630-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20356"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20357"><span class="mi" id="MathJax-Span-20358" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20359" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20360" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20361" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20362" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20363" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20364" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20365" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20366" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-20367" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20368" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20369" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20370" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20371" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20372" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20373" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-630">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 class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview">r</span><span class="MathJax MathJax_Processing" id="MathJax-Element-631-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-631">r</script>  and  <span class="MathJax_Preview">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-632-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-632">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview">r</span><span class="MathJax MathJax_Processing" id="MathJax-Element-633-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-633">r</script>  and  <span class="MathJax_Preview">s</span><span class="MathJax MathJax_Processing" id="MathJax-Element-634-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-634">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-635-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-635">\begin{array}[t]{l}
+<div class="constraint" number="53" id="impossible-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-property-overlap">Constraint 53 (impossible-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-631-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20374"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20375"><span class="mi" id="MathJax-Span-20376" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.5px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-631">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-632-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20377"><span style="display: inline-block; position: relative; width: 1171px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20378"><span class="mi" id="MathJax-Span-20379" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-20380" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mo" id="MathJax-Span-20381" style="font-family: STIXGeneral-Regular; padding-left: 6px;">{</span><span class="mi" id="MathJax-Span-20382" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20383" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20384" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20385" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20386" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20387" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20388" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20389" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20390" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-20391" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20392" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20393" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20394" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20395" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20396" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20397" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20398" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20399" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20400" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20401" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20402" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20403" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20404" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20405" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-20406" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20407" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20408" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20409" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20410" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20411" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20412" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20413" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20414" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20415" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20416" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20417" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20418" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20419" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20420" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20421" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20422" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-20423" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20424" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20425" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20426" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20427" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20428" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20429" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20430" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20431" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20432" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20433" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20434" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20435" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20436" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20437" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20438" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20439" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20440" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20441" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20442" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20443" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20444" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20445" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20446" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-20447" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20448" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-20449" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20450" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20451" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-20452" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20453" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20454" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20455" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20456" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20457" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20458" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20459" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20460" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-20461" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20462" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20463" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20464" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20465" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-20466" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20467" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20468" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20469" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20470" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-20471" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-20472" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20473" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20474" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20475" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20476" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-20477" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20478" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20479" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20480" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20481" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20482" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20483" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20484" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20485" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20486" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-20487" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20488" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20489" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-20490" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20491" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20492" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20493" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20494" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20495" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20496" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20497" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20498" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20499" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20500" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-20501" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20502" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20503" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-20504" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20505" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20506" style="font-family: STIXGeneral-Regular;">}</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-632">s \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script> such that <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-633-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20507"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20508"><span class="mi" id="MathJax-Span-20509" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.5px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-633">r</script>  and  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-634-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20510"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20511"><span class="mi" id="MathJax-Span-20512" style="font-family: STIXGeneral-Italic;">s</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-634">s</script> are different relation names, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-635-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20513"><span style="display: inline-block; position: relative; width: 303px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.2px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20514"><span class="mtable" id="MathJax-Span-20515" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 297px; height: 0px;"><span style="position: absolute; clip: rect(67.8px 19360px 138.2px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 297px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 54px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20516"><span class="mrow" id="MathJax-Span-20517"><span class="mi" id="MathJax-Span-20518" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20519" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20520" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20521" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20522" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20523" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20524" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20525" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20526" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20527" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20528" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 21.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20529" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20530" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">m</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20531" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20532" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20533" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20534" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20535" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20536" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20537" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20538" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20539" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20540" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20541" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20542" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-20543"><span class="mrow" id="MathJax-Span-20544"><span class="mspace" id="MathJax-Span-20545" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20546" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-20547" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20548" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20549" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20550" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20551" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20552" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20553" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20554" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20555" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20556" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20557" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 21.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20558" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20559" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">m</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20560" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20561" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20562" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">s</span><span class="mo" id="MathJax-Span-20563" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20564" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20565" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20566" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20567" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20568" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20569" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20570" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20571" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20572" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20573" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20574" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20575" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20576" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 1.3px; left: 0px;"><span class="mtd" id="MathJax-Span-20577"><span class="mrow" id="MathJax-Span-20578"><span class="mspace" id="MathJax-Span-20579" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20580" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20581" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20582" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20583" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20584" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20585" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 71.7px; vertical-align: -55.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-635">\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)
@@ -3493,14 +2883,7 @@
   interactions are disjoint sets, characterized by their types.
   </p>
   </div>
-<div class="constraint" number="54" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview">p \in \{entity,activity,agent\}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-636-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-636">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-637-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-637">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script>, the following constraint holds:</p><span class="MathJax_Preview">\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}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-638-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-638">\begin{array}[t]{l}
+<div class="constraint" number="54" id="impossible-object-property-overlap"><div class="ruleTitle"><a class="internalDFN" href="#impossible-object-property-overlap">Constraint 54 (impossible-object-property-overlap)</a></div><p>For each <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-636-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20586"><span style="display: inline-block; position: relative; width: 205px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20587"><span class="mi" id="MathJax-Span-20588" style="font-family: STIXGeneral-Italic;">p</span><span class="mo" id="MathJax-Span-20589" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mo" id="MathJax-Span-20590" style="font-family: STIXGeneral-Regular; padding-left: 6px;">{</span><span class="mi" id="MathJax-Span-20591" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20592" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20593" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20594" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20595" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20596" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20597" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20598" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20599" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20600" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20601" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20602" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20603" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20604" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20605" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20606" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20607" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20608" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-20609" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20610" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20611" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-20612" style="font-family: STIXGeneral-Regular;">}</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-636">p \in \{entity,activity,agent\}</script>  and each <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-637-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20613"><span style="display: inline-block; position: relative; width: 1172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20614"><span class="mi" id="MathJax-Span-20615" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-20616" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mo" id="MathJax-Span-20617" style="font-family: STIXGeneral-Regular; padding-left: 6px;">{</span><span class="mi" id="MathJax-Span-20618" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20619" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20620" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20621" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20622" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20623" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20624" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20625" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20626" style="font-family: STIXGeneral-Italic;">G</span><span class="mi" id="MathJax-Span-20627" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20628" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20629" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20630" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20631" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20632" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20633" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20634" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20635" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20636" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20637" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20638" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20639" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20640" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20641" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-20642" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20643" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20644" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20645" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20646" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20647" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20648" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20649" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20651" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20652" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20653" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20654" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20655" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20656" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20657" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20658" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-20659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20660" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20661" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20662" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20663" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20664" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20665" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20666" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20667" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20668" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20669" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20670" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20671" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20672" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20673" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20674" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20675" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20676" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20677" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20678" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20679" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20680" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20681" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20682" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-20683" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20684" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-20685" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20686" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20687" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-20688" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20689" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20690" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20691" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20692" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20693" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20694" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20695" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20696" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-20697" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20698" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20699" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20700" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20701" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-20702" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-20703" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20704" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20705" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20706" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-20707" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-20708" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20709" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">w</span><span class="mi" id="MathJax-Span-20710" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20712" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-20713" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20714" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20715" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20716" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20717" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20718" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20719" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20720" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20721" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20722" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-20723" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20724" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20725" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-20726" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20727" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20728" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20729" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20730" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20731" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-20732" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20733" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20734" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-20735" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20736" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-20737" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20738" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20739" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-20740" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20741" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20742" style="font-family: STIXGeneral-Regular;">}</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 19.2px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-637">r \in \{ used, wasGeneratedBy, wasInvalidatedBy, wasStartedBy, wasEndedBy, wasInformedBy, wasAttributedTo, wasAssociatedWith, actedOnBehalfOf\}</script>, the following constraint holds:</p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-638-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20743"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.7px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20744"><span class="mtable" id="MathJax-Span-20745" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 300px; height: 0px;"><span style="position: absolute; clip: rect(67.8px 19360px 138.7px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 300px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 54px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20746"><span class="mrow" id="MathJax-Span-20747"><span class="mi" id="MathJax-Span-20748" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20749" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20750" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20751" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20752" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20753" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20754" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20755" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20756" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20757" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20758" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 21.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20759" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20760" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">m</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20761" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20762" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20763" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20764" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20765" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20766" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20767" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20768" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20769" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20770" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20771" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20772" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23px; left: 0px;"><span class="mtd" id="MathJax-Span-20773"><span class="mrow" id="MathJax-Span-20774"><span class="mspace" id="MathJax-Span-20775" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20776" style="font-family: STIXGeneral-Italic;">p</span><span class="mo" id="MathJax-Span-20777" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20778" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20779" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20780" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20781" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20782" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20783" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20784" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20785" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20786" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20787" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 21.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20788" style="font-family: STIXGeneral-Italic;">a</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20789" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">m</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20790" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20791" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20792" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-20793" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20795" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20796" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-20797" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20798" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mn" id="MathJax-Span-20799" style="font-size: 70.7%; font-family: STIXGeneral-Regular;">1</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20800" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-20801" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">…</span><span class="mo" id="MathJax-Span-20802" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">,</span><span class="msubsup" id="MathJax-Span-20803" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.2px -8.6px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20804" style="font-family: STIXGeneral-Italic;">b</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 10px;"><span class="mi" id="MathJax-Span-20805" style="font-size: 70.7%; font-family: STIXGeneral-Italic;">n</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span><span class="mo" id="MathJax-Span-20806" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 1.9px; left: 0px;"><span class="mtd" id="MathJax-Span-20807"><span class="mrow" id="MathJax-Span-20808"><span class="mspace" id="MathJax-Span-20809" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20810" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20811" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20812" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20813" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20814" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20815" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72.2px; vertical-align: -55.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-638">\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)
@@ -3513,14 +2896,7 @@
   from other objects (entities, activities or agents).
   </p>
   </div>
-<div class="constraint" number="55" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall id.~
-\\
-\qquad typeOf(id,entity) \wedge typeOf(id,activity)
-\\
-\quad\Rightarrow
-False
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-639-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-639">\begin{array}[t]{l}
+<div class="constraint" number="55" id="entity-activity-disjoint"><div class="ruleTitle"><a class="internalDFN" href="#entity-activity-disjoint">Constraint 55 (entity-activity-disjoint)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-639-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20816"><span style="display: inline-block; position: relative; width: 342px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 97px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20817"><span class="mtable" id="MathJax-Span-20818" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 336px; height: 0px;"><span style="position: absolute; clip: rect(66.8px 19360px 136px -9px); top: -83px; left: 0px;"><span style="display: inline-block; position: relative; width: 336px; height: 0px;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20819"><span class="mrow" id="MathJax-Span-20820"><span class="mi" id="MathJax-Span-20821" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20822" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20823" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20824" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20825" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -24.8px; left: 0px;"><span class="mtd" id="MathJax-Span-20826"><span class="mrow" id="MathJax-Span-20827"><span class="mspace" id="MathJax-Span-20828" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20829" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20830" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-20831" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20832" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20833" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20834" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20835" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20836" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20837" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20838" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20839" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-20840" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-20841" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20842" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20843" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20844" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20845" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20846" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20847" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20848" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-20849" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20850" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20851" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20852" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20853" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20854" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20855" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mo" id="MathJax-Span-20856" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20857" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-20858" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20859" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20860" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20861" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-20862" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20863" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20864" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-20865" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 0.2px; left: 0px;"><span class="mtd" id="MathJax-Span-20866"><span class="mrow" id="MathJax-Span-20867"><span class="mspace" id="MathJax-Span-20868" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20869" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20870" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20871" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20872" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20873" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20874" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 83px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 70.5px; vertical-align: -54px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-639">\begin{array}[t]{l}
 \forall id.~
 \\
 \qquad typeOf(id,entity) \wedge typeOf(id,activity)
@@ -3532,14 +2908,7 @@
   <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 class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview">\begin{array}[t]{l}
-\forall c,e.~
-\\
-\qquad hasMember(c,e) \wedge typeOf(c,prov:EmptyCollection)
-\\
-\quad\Rightarrow
-False
-\end{array}</span><span class="MathJax MathJax_Processing" id="MathJax-Element-640-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-640">\begin{array}[t]{l}
+<div class="constraint" number="56" id="membership-empty-collection"><div class="ruleTitle"><a class="internalDFN" href="#membership-empty-collection">Constraint 56 (membership-empty-collection)</a></div><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-640-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20875"><span style="display: inline-block; position: relative; width: 460px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.5px 19360px 98.5px -5.8px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20876"><span class="mtable" id="MathJax-Span-20877" style="padding-right: 3.2px; padding-left: 3.2px;"><span style="display: inline-block; position: relative; width: 454px; height: 0px;"><span style="position: absolute; clip: rect(68.2px 19360px 138.5px -9px); top: -84px; left: 0px;"><span style="display: inline-block; position: relative; width: 454px; height: 0px;"><span style="position: absolute; clip: rect(32.2px 19360px 53.7px -9px); top: -48px; left: 0px;"><span class="mtd" id="MathJax-Span-20878"><span class="mrow" id="MathJax-Span-20879"><span class="mi" id="MathJax-Span-20880" style="font-family: STIXGeneral-Regular;">∀</span><span class="mi" id="MathJax-Span-20881" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-20882" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20883" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-20884" style="font-family: STIXGeneral-Regular;">.</span><span class="mtext" id="MathJax-Span-20885" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">&nbsp;</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(31.8px 19360px 55px -9px); top: -23.3px; left: 0px;"><span class="mtd" id="MathJax-Span-20886"><span class="mrow" id="MathJax-Span-20887"><span class="mspace" id="MathJax-Span-20888" style="height: 0px; vertical-align: 0px; width: 43.6px; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-20889" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-20890" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20891" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20892" style="font-family: STIXGeneral-Italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-20893" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20894" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-20895" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-20896" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20897" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-20898" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20899" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-20900" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20901" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-20902" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-20903" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">∧</span><span class="mi" id="MathJax-Span-20904" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20905" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-20906" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20907" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20908" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-20909" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-20910" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-20911" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-20912" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-20913" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-20914" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20915" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20916" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-20917" style="font-family: STIXGeneral-Regular; padding-left: 6px;">:</span><span class="mi" id="MathJax-Span-20918" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20919" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-20920" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-20921" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20922" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-20923" style="font-family: STIXGeneral-Italic;">C<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-20924" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20925" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20926" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20927" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-20928" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-20929" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-20930" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-20931" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-20932" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-20933" style="font-family: STIXGeneral-Regular;">)</span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; clip: rect(32.8px 19360px 52.9px -9px); top: 1.6px; left: 0px;"><span class="mtd" id="MathJax-Span-20934"><span class="mrow" id="MathJax-Span-20935"><span class="mspace" id="MathJax-Span-20936" style="height: 0px; vertical-align: 0px; width: 21.8px; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-20937" style="font-family: STIXGeneral-Regular;">⇒</span><span class="mi" id="MathJax-Span-20938" style="font-family: STIXGeneral-Italic; padding-left: 6px;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-20939" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-20940" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-20941" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-20942" style="font-family: STIXGeneral-Italic;">e</span></span></span><span style="display: inline-block; width: 0px; height: 49px;"></span></span></span><span style="display: inline-block; width: 0px; height: 84px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 72px; vertical-align: -55.5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-640">\begin{array}[t]{l}
 \forall c,e.~
 \\
 \qquad hasMember(c,e) \wedge typeOf(c,prov:EmptyCollection)
@@ -3562,30 +2931,30 @@
 
 </p><div class="theorem" id="soundness" data-count="32" data-title="Theorem 32 (soundness)"><div class="ruleTitle"><a class="internalDFN" href="#soundness">Theorem 32 (soundness)</a></div>
   <ol>
-  <li>If <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-641-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-641">I</script> is an instance and <span class="MathJax_Preview">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-642-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-642">W \models I</script> and <span class="MathJax_Preview">I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-643-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-643">I'</script> is obtained from <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-644-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-644">I</script> by applying one
-  of the PROV inferences, then <span class="MathJax_Preview">W \models I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-645-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-645">W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-646-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-646">I</script> is an instance and <span class="MathJax_Preview">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-647-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-647">W \models I</script> then <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-648-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-648">I</script> has a normal
-  form <span class="MathJax_Preview">I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-649-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-649">I'</script> and   <span class="MathJax_Preview"> W \models I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-650-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-650"> W \models I'</script>.</li>
-  <li>If <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-651-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-651">I</script> is a normal form and <span class="MathJax_Preview">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-652-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-652">W \models I</script> then <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-653-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-653">I</script> satisfies all of the ordering,
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-641-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20943"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20944"><span class="mi" id="MathJax-Span-20945" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-641">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-642-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20946"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20947"><span class="mi" id="MathJax-Span-20948" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-20949" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-20950" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-642">W \models I</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-643-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20951"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.9px 19360px 44px -9.2px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20952"><span class="msup" id="MathJax-Span-20953"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20954" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-20955" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.1px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-643">I'</script> is obtained from <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-644-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20956"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20957"><span class="mi" id="MathJax-Span-20958" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-644">I</script> by applying one
+  of the PROV inferences, then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-645-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20959"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.9px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20960"><span class="mi" id="MathJax-Span-20961" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-20962" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="msup" id="MathJax-Span-20963" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20964" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-20965" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-645">W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-646-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20966"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20967"><span class="mi" id="MathJax-Span-20968" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-646">I</script> is an instance and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-647-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20969"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20970"><span class="mi" id="MathJax-Span-20971" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-20972" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-20973" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-647">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-648-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20974"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20975"><span class="mi" id="MathJax-Span-20976" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-648">I</script> has a normal
+  form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-649-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20977"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.9px 19360px 44px -9.2px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-20978"><span class="msup" id="MathJax-Span-20979"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20980" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-20981" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.1px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-649">I'</script> and   <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-650-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20982"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.9px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20983"><span class="mi" id="MathJax-Span-20984" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-20985" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="msup" id="MathJax-Span-20986" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-20987" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-20988" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-650"> W \models I'</script>.</li>
+  <li>If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-651-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20989"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20990"><span class="mi" id="MathJax-Span-20991" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-651">I</script> is a normal form and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-652-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20992"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20993"><span class="mi" id="MathJax-Span-20994" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-20995" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-20996" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-652">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-653-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-20997"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-20998"><span class="mi" id="MathJax-Span-20999" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-653">I</script> satisfies all of the ordering,
   typing and impossibility constraints.
-  </li><li>If <span class="MathJax_Preview">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-654-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-654">W \models I</script> then <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-655-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-655">I</script> is valid.</li>
+  </li><li>If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-654-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21000"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21001"><span class="mi" id="MathJax-Span-21002" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-21003" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-21004" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-654">W \models I</script> then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-655-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21005"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21006"><span class="mi" id="MathJax-Span-21007" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-655">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">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-656-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-656">I</script> is in normal form them we are
-  done. If <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-657-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-657">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">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-658-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-658">W \models I</script> the uniqueness constraint cannot
-  fail on <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-659-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-659">I</script> and <span class="MathJax_Preview">W \models I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-660-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-660">W \models I'</script>.</p>
+  or uniqueness constraint steps: if <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-656-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21008"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21009"><span class="mi" id="MathJax-Span-21010" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-656">I</script> is in normal form them we are
+  done. If <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-657-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21011"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21012"><span class="mi" id="MathJax-Span-21013" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-657">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 class="MathJax" id="MathJax-Element-658-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21014"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21015"><span class="mi" id="MathJax-Span-21016" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-21017" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-21018" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-658">W \models I</script> the uniqueness constraint cannot
+  fail on <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-659-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21019"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21020"><span class="mi" id="MathJax-Span-21021" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-659">I</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-660-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21022"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.9px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21023"><span class="mi" id="MathJax-Span-21024" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-21025" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="msup" id="MathJax-Span-21026" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-21027" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-21028" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-660">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">W \models I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-661-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-661">W \models I</script>.  Then <span class="MathJax_Preview">W \models I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-662-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-662">W \models I'</script> where <span class="MathJax_Preview">I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-663-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-663">I'</script> is the normal
-  form of <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-664-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-664">I</script> by part 2.  By part 3, <span class="MathJax_Preview">I'</span><span class="MathJax MathJax_Processing" id="MathJax-Element-665-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-665">I'</script> satisfies all of the
-  remaining constraints, so <span class="MathJax_Preview">I</span><span class="MathJax MathJax_Processing" id="MathJax-Element-666-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-666">I</script> is valid.</p>
+  suppose <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-661-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21029"><span style="display: inline-block; position: relative; width: 49px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21030"><span class="mi" id="MathJax-Span-21031" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-21032" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-21033" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 15.2px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-661">W \models I</script>.  Then <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-662-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21034"><span style="display: inline-block; position: relative; width: 57px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.9px 19360px 51.3px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21035"><span class="mi" id="MathJax-Span-21036" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-21037" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="msup" id="MathJax-Span-21038" style="padding-left: 6px;"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-21039" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-21040" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.4px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-662">W \models I'</script> where <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-663-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21041"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.9px 19360px 44px -9.2px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-21042"><span class="msup" id="MathJax-Span-21043"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-21044" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-21045" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.1px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-663">I'</script> is the normal
+  form of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-664-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21046"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21047"><span class="mi" id="MathJax-Span-21048" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-664">I</script> by part 2.  By part 3, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-665-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21049"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(22.9px 19360px 44px -9.2px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-21050"><span class="msup" id="MathJax-Span-21051"><span style="display: inline-block; position: relative; width: 14.7px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-21052" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -49.4px; left: 8.3px;"><span class="mo" id="MathJax-Span-21053" style="font-size: 70.7%; font-family: STIXVariants;">′</span><span style="display: inline-block; width: 0px; height: 42px;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 17.1px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-665">I'</script> satisfies all of the
+  remaining constraints, so <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-666-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-21054"><span style="display: inline-block; position: relative; width: 7px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.4px 19360px 51px -9.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-21055"><span class="mi" id="MathJax-Span-21056" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 14.6px; vertical-align: -1px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-666">I</script> is valid.</p>
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